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Exponentials PART 2 - Matching Exponential Equations to Graphs

Added Jan 10, 2023 •

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Exponentials PART 2 - Matching Exponential Equations to Graphs

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what's going on y'all it's a math teacher Miss Harris and I'm back with another video alright so today we are working on EQ 11 part 2 A Part 2 when does Morgan talk about matching exponential equations to the graph and we're going to talk about exponential growth and exponential decay finding that growth factor of that decay factor and finding the growth rate for the Decay rate okay so go ahead you already know get your note get a pencil and less getting so it so there's no worry while today so I can for y'all we're going to just jump right into that lesson with which equation matches the graph and I know what you're thinking we're going to have to plug in eggs for this exponent every single time for every single one of these equations absolutely know what you are going to do if you're going to take your ex okay you're going to look for that x value on the graph okay and then you just going to feel in what why it's with it is X okay nothing to say was I'm talking about that way is going to be easier for you to figure out your pattern and then you guys can go ahead and see like this is the equation that matches the graph all right start with x equals negative 3x - 4 - 5 - 3 on Minecraft here it is -3 K to the Peace of the graph if you. kids hats 8 Stone -3 goes with 8 so that's why I'm going to spill into the table. Uh-oh. Let's try and -2 if x is equal to -2 we're going to die. Up. Up. Up. oh my goodness it matches up with positive for all right then -1 a -1 of a buck that it matches up with 20 oh here it is we are at 1 and 4 a positive one up above where that about half and then two of them were bad at 1/4 okay and I'm really honestly doing it because I already know the pattern if you notice a pattern awesome I hope you guys are like yelling at the screen if not it's okay but see what it is. If you notice we're going from a 4 to 2 so 12 1/2 to 1/4 do you guys like I need to know what operation that is well we're obviously not going to be subtracted we know we're getting smaller but it's 44 - 4 doesn't give you 2 + 2 - 4 do is not subtracting okay it's not subtracting what other operation is going to give us a smaller number every single time down the chart it's me dividing so 8 / what is going to 424 / what is going to give you two is too soon about about what is going to give you one as soon as you can Otis Redding / 2D whole way down and I need you to know that / 2 is cutting something in half okay so obviously we're not going to have a obviously we're not going to have B because it's telling you that our exponential factor is going to be one or two which is not true at all that's not we have to cut in half so our gross back there are Decay right there where Happening Here is 1/2 okay so are we starting at 2 is our initial value to remember your initial value write this down is what y equals when x equals 0 there when x equals 0 here that matches up with one Saudi can't be it either so your answer has to be Cy equals 1/2 x because obviously your pattern is divided by 2 or cutting and a half or * 1/2 so that's going to be the equation that matches the graph okay it is again but with another type of graph it we can this time is going from bottom to top let's see what's happening with these ordered pairs okay so if I start at The X, okay I'm going to look for this on the x-axis anyway these numbers and I'm just going to match it up with the y coordinate okay so I started - 24 - here it is Bubba Buck I'm at about 1/4 -1 1/2 Z-Ro I'm at 11 I'm at 2 dude I'm at 4 and 3 I'm at this one is really easier to see just because I like you can see when something is doubling way easier than you can clean it like being cut in half so we know that 1 * 2 is going to give us too we know that 2 * 2 and give us for we know that 4 * 2 is still going to give us a OK and even 1/4 * 2 you want me to do that I will 14 * 2 + 2 or 11 * 2 is Dubois has one was for now I know you're saying is here divorce divorce can be simplified on boy homegirl 2 1/2 games that works okay the 1/2 * 2 or 2:01 is going to give us to over to which simplifies to one so that works as well let means that our our growth factor our pattern is having everything else I'm going to have the X to will you look at the number in parentheses that is the number that you are going to X every single time if you look at all these if you look at that you're going to be * 1 that's how we want if you look at Steve we're going * 1/2 that's not what we want if you look at D we're going to be most unhappy again that's not what we want so the only choice is be okay because I what is happening here is that the number we're starting with is that invisible Warren and remember that your initial value where you start where x equals 0 y equals 12 1 times are growth factor of 2 which is what's happening every single time so that's why I be is our answer okay let's go ahead and move on if you have questions about that please go ahead and ask me when we do our live less than or email me or text me via remind if you do not understand what I just did right alright let's move into exponential growth exponential decay so now you have seen it on a grab now I'm about to see you it looks like with an equation with a formula okay you got something a little bit new here so I know this is going to take us but I want you guys to write down what you see on the screen I know it's okay but I promise you this is going to help you once you guys go back and you study before you take your EQ 11 quiz okay so I want you to take a minute and I want you to pause your screen I want you to write down what you see in the boxes and I will did you write down what you see as far as the bullet point in the blue make sure this is nice and neat this is going to be your tips it's going to be your help this guy have your support for when we do exponential growth and Decay okay these are your helpers here the please write them down nice and neatly imma go ahead and I'm going to show you how to apply this to your equation ke Rog dhara dihala I was in pool okay so I need you guys to understand that we're still starting with y equals a x b to the X power okay where y equal stays the same you're a is your initial value your wine in a number where you start whatever you want to call it as long as you know where you start at the beginning that's all that matters okay and then B is going to be your base number that's going to be your gross Factory that's going to indicate whether you're going to increase get bigger or decrease your smaller okay pics of course that's where your exponents so what I need for you to remember also about be is that when it's an exponential growth your behalf to be bigger than one it has to be bigger than one okay with your exponential decay your B has to be bigger than 0 but it has to be smaller than one so I had to be some kind of decimal okay some kind of zero point something something something but it cannot equal up the 10K all right so what's going to happen is we are going to rewrite y equals 8 with this new equation I just highlighted in yellow now the reason why we are doing this is because we want to find our growth rate we actually want to know what it is growing by what percentage what decimal whatever maybe I'm going to show you that step by step OK Google start with the one on the left so you start off with y equals 8 * B to the X where you know that he has to be bigger than 10 we're going to replace that be with this special little expression that is 1 + are in the parentheses now OnePlus are it's just your OnePlus your common ratio plus your be okay plus your growth factor it was going to happen is if we rewrite be as 1 + are we can determine what the Roserade is actually going to be and are as it's really going to be a percentage or it's going to be written as a decimal so if you look at this example right here you got y equals 2 * 1.43 to the X power Okay so this means that your growth factor is going to be and I had this as a pen again please okay you're going to have your gross back door which of course is the number that's in parentheses is going to be 1.43 then your growth rate going to be hang on one second doing the video are y'all I'm back I am so sorry I've got plenty of visitors today but I am back to go ahead and back into it so I was talking about y equals 8 * 1 + r to the X power and we were just picking out with our growth factor with our girls writing with our initial value okay the growth factor was obviously what we are X that's our Base number so it's 1.43 or actual growth rate so what's going to happen is that you guys are going to have to subtract 1 - 1. 43k which is going to give you - 0.43 but what I want you to realize here is that in your calculator you do the absolute value of this okay if we just want to be at what is the absolute value of our growth rate that we can turn it in so when you have a -2.43 when you take the absolute value of that that's actually going to give you a positive 0.43 cuz that our growth rate that's the actual percentage that it is increasing by okay and then our initial value the fur number that you see where you start it's going to be positive to all right alright so let's go ahead and do the next ones that once again we're going to start off with y equals 8 x be today but then I'm going to replace be with 1 - are all right so what's going to happen is we're going to try and find the Decay rate this time and so I'm going to start with what I actually know I'm going to start my Decay back after I see my BK factors is the number that since I I pray it stays within which is 0.75 then I need to do one -0.75 to figure out my Decay rate is like saying $1 - $0.75 which gives me one quarter or 25 seconds left. 25 and then mine is about you just the first number that you see in this equation is going to be 300 really super simple really super easy the main thing I need to remember with finding that growth rate for the Decay rate if it is negative you have to have pause the number so you need to find the absolute value of even if it's positive the absolute value of it is still going to be positive if it's negative the absolute value of it it's going to be positive. Please remember to ask who that is going to be your friend when you're trying to find the growth were Decay rate let's go ahead and move on Lennox parts are you going to go next example so given the following in Gross function so this y equals 2 * 1.5 to the X power we're going to use to take with you sketch the graph and answer the questions below so what's going to happen here is that I am actually going to feel in the bottom part I want to fill in my growth factor which I can find from this equation right here my girls back then once again is going to be that number that's in parentheses or was 1.5 my growth rate once again remember is going to be the absolute value of 1 - whatever my growth factor is a 1 - 1 which is going to give me -0.5 Members got to be the absolute value so that's going to make it a positive 0.5 K that start with this which is 2 the nail what I'm going to do is I am going to fill in this table next so here I go what's going to happen is I am going to just plug in some numbers that will be easy to graph on this Courtney playing here so I'm going to plug in one two and three am I going to plug into negative so you guys can see how that's going to work so I'm going to plug in -1 and -2 is well okay so these exits of course are going to be plugged in or ex right here so I am erase what I have that way you guys can see my work alright baby I'm going to start with y equals 2 * 1.5 to the but instead of that X let me go ahead and start with one so you got 2 * 1.5 to the first Power where do are exponents first just because of order of operations okay so what's going to happen. I'm going to do 1.5 to the first Power which is going to be 1.56 lb 2 * 1.5 which is going to equal 3 okay so that means that when x equals 1 Y is going to equal 3 all right so we can do the same thing but this erase and I choose a different exponents go to my calculator ready to go back and show you what we got to do all right so now we're going to plug in so we are going to do 1.5 squared + 1.5 * 1.5 which is going to give me 2.25 and I'm getting * 2 that's going to give me 4.5 K so when x equals 2y is going to equal 4.5 we're going to do this one more time and we are going to do how to get rid of that too now we're going to plug in the three all right so now we're going to be 1.5 cubes so that's going to be 1.5 * 1.5 * 1.5 which is going to give me 3.375 and we're going to multiply that by 2 forgot what I was going to be so our why is going to be 6.75 when you're x equals 3 so when your phone is 3 okay bed backwards here we go we're going to start with an egg it is all right so the easiest way for me to go ahead and do these negative job is just to go ahead and plug all of it into the calculators that once you plug this whole equation in with your front of neck you should get the answer of 4/3 and we'll grab that and then same thing with negative two when you plug it in for X with your whole entire question you should get the answer of 8 night at your head and grab all of that I'll grab the phone number to ninja draw a line for the rest of this really hard to estimate fractions when you're doing an exponential function graph so we're going to start with 0 + 2 x equals 0 y equals 2 when x equals 1 y equals 3 when x equals 2y equals 4.5 something like right here okay and then when x equals 3 why is going to equal 6.7 a really close today at 7 are you trying to get there. Just leave it right there we go all right and then really get that I can graph I'm just going to estimate the rest of here is your exponential function and also will funky but you guys can see it okay I'm going to scoop the rest of it down estimated okay so this is really what your graph is going to look like on let's go ahead and do the next one we got to y equals 2 * 1/3 to the X power so once again I'm just going to plug some easy points that should be able to grab so I've got one two and three and I've got - -2 okay so what I'm going to do is plug Annex the number that I put four eggs for my exponent and then I am going to I'm going to plug it in so I can figure out why it's going to be okay let's start off with negative two so when you have - 2 you're going to have y equals 2 * 1/3 to the negative 2nd power now remember when you have a negative effects on you got to change your fraction got to flip it to it's reciprocal so you're going to have y equals 2 * 3 squared we all know the three where does the same thing as 3 * 3 which gives you 9 and we all know that two times nine is going to give me 18K. When x equals negative 2 y equals 18 what do the same thing but when negative one here so we got why 2 * 1/3 to the negative 1 power which is really going to be y equals 2 * 3 to the first Power was just three so that means that white was 2 * 3 which is 6 let me know when x equals 0 y equals 2 now let's go ahead and plug in my whole numbers and I've got y equals 2 * 1/3 to the 1st power such as y equals 2/1 * 1/3 is it going to be two-thirds cuz I hear there's nothing in y equals 2 * 1/3 Square which is it is going to be 1/3 * 1/3 / 1/3 that's one-third okay so then we're just going to multiply straight across 2 * 1 * 1 is going to get his me to then 1 x 3 x 3 is going to give me nice I'm going to have two nights okay we're going to do the same thing one more time but this time when I plug in 3 y equals 2 * 1/3 Q which is the same thing as y equals 2/1 * 1/3 * 1/3 * 1/3 * 2 * 1 * 1 * 1 2 * 1 * 3 * 3 * 3 can you give me 27th and my answer is going to be 2/27 of course I cannot grab all of that so I'm just going to estimate a lot of it but just hang in there with me I will try and grab as much as I can for you I'm trying to race on a race give me a second this is a lot to erase without erasing everything come on, we're almost there, Ghana I'm trying to grab this exponential function change color alright so let's start with a - 2 so when x - 2y is going to eat play things that you can't really grasp that so I'm just going to start with an arrow does going to represent the 18 is all the way up there and then when x equals negative one was going to equal sticks I'm going to start my arrow and follow it through here okay then when x equal 0 wise going to equal to do something to keep on going by line hey if you noticed is going from top to bottom so you know what the Decay then I'm going to go when x equals one was going to go to Thursday about right right here going to start the car and the rest I really cannot drop you guys exactly so I'm just going to estimate and going and curve that thing on out okay but I got to be at my Decay Factor my right and my initial value okay so what's happening here is that my Decay factor is number 2 in parentheses so that's one-third I know my initial value where I start is going to be 2 and then I've got to figure out what is going on every single time now I know you guys can't really see what's happening here but it is dividing by 3 every single time what's happening is is that it's not just divided by 3 but it's actually the came by 2/3 because what you also want to do is that 1 - 1/3 remember the absolute value of 1 - 1/3 is going to give you two so that's what's going to make your Decay right okay alright let's go ahead and move on to the next part are exponential functions practice all right so we can do this real quick I am going to do one the next one through six with you guys I'm but I'm going to like do one through three with you and then four five and six you guys are going to try on your own it and then we'll be done for the day but here we go number 1 the first thing you want to know is it a growth or decay I do remember for it to be a growth it has to be the number in parentheses has to be a bigger than one since I have a decimal of .25 that's between 0 and 1 so that's actually going to be a Decay my initial value that's just the number that I start at is going to be 10K my growth or Decay factor is just a number that's in parentheses or it's going to be 1 to 5 and then how do you find your growth or Decay rate remember you're going to do the absolute value of 1 - are so that's going to be absolute value of 1 - 0.25 which is going to be 0.75 okay so that is my Decay right okay let's go ahead and try number two so this time I've got y equals you're a ninja body what you can't see is just an invisible 1 * 5 to the X power so since your number that's in the parentheses bigger than one that is a growth your initial value once again you cannot see it's an invisible one your growth or Decay factor is the number that's inside the parentheses so that's five and then your growth or Decay rate so that's going to be once again the absolute value of 1 - whatever is in parentheses or 1 - 5 is going to give you a negative or but the absolute value of 9 or is going to be for the 4 or if you want to write that as a percentage you would just do that decimal two times to the right there's going to be or hundred percent okay number three yes practice real quick if you're going to have y equals 2.5 * 2 to the X power your number in parentheses is bigger than one so that's going to be a gross exponential growth Decay your initial value is going to be the first number you see is 0.5 a your growth or Decay factor is the number that's inside the parentheses which is two then you're going to do your absolute value 1 - r 1 - 2 wood gives you a negative one the value of -1 is 10 K don't want you guys to practice with four five and six let's start with Forester pause your screen try answering each one of these questions and then we'll check it real quick all right let's go ahead and check number for here we go all right so you got to look at your growth or Decay look at the number that's inside the parentheses this is a decimal which is between 0 and 1 so that means it's going to be a Decay your initial value is going to be the first time you see so it's going to be 9 your growth the K-factor going to be the number is inside the parentheses which is 0.7 and then your growth or Decay rate that's where you come in with the absolute value of 1 - are just going to be the absolute value of 1 - 0.67 which is going to be the absolute value of 0.3 which is obviously 0.3 or if you want to turn that into a percentage that is 30% in case if you got that right great job off my awesome all right now 5 you got y equals 4 * 2/3 to the Exxon ^ your screen go ahead and try it and then we will check it to you are you we go so growth or Decay the number that's inside of Prince is a fraction but if you change a fraction to a decimal is going to be 0.6 + 6 + 6 + 6 + 6 repeating or 0.67 which is between 0 and 1 so that means it's going to be a  hey okay your initial value is the first WC which is where your growth or Decay factor is the number that's inside the parentheses which is 2/3 day and then your growth or Decay rate is going to be that an absolute value of 1 - are you done it's the main one time y'all 1 - 2 1 - 2/3 going to give us absolute value of 1/3 which is still going to be positive 1/3 if you got that right awesome awesome I'm going to tell you I don't want you to do is I want you to set this up so I'm even give you the formula you're supposed to use of us to use y equals a Time 1 + r to the X power on the plug-in what you know okay I was just going to try it and then we'll check it all right here we go so we know that a is going to represent our first term or the first number that we see which is going to be our starting point or initial value or Y intercept whatever you want to call it so where do we start an iguana I'm sorry in a Guana Isabel Ortiz 2 cm at Birth the when it's born that's what what link is start that means your day is going to be or D 2 times and then you're going to have our rate our rate of 12% now I want to chat 12% into a decimal don't take that % we're just going to make that 12 and if Scooby wants to be twice to the left that's going to be 1 + 0.12 to the 8th power then I'm going to simplify this I can add and plus you're going well and I have y equals 42 * 1.12 to the X power and that is my answer so if you got that right congratulations awesome awesome awesome job IND is the end of part 3 we have made it once again you guys are going to have an assignment that goes along with this video you guys are going to have some Delta math that you can practice with if you did not get it and of course it's always there will be a live lesson I will let you guys know what day I will let that's no the link that way you guys can come in and join and ask whatever questions that you have you can just get more one-on-one attention I can float the exam for you but thanks for hanging in there as always I love you guys you got to do an awesome we are so close to the Finish I keep saying this every week you guys are almost sophomores and I am so so so so proud of you email me if you need me text me the remind if you need me but until then I hope you guys have a wonderful day and I will talk to y'all later

Uploaded by Kristen Harris.

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Exponentials PART 2 - Matching Exponential Equations to Graphs

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