Videos

Exponential Functions - Delta Math Help

Added Jan 22, 2023 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//lhs.rcschools.net/apps/embed/?v=349825" frameborder="0" allowfullscreen></iframe> Change dimensions

Exponential Functions - Delta Math Help

Show Transcript

what's going on yeah it's the math teacher Miss Harris and I'm back with another so today we are going to go over some of the things that you guys have already learned a exponential function and I help you with your Delta math because I know there are a couple of things that you and I are your other teachers have not gotten to yet so I'm going to do my best to try and teach is really really fast and show you something that you may not have seen yet when it comes exponential functions that way. I can get this done if you can be successful on it so just go ahead and grab your notes real quick I promise I'm going to try to make it to your like 10 minutes or less so here we go you already know what to do grab your pistol notebook make sure you dry everything that you need to draw anything that's going to help you with this Delta math please go ahead and do it now so that way you're not stuck or needing help later on and let's get into it so the first thing if I could hide this something quick no thanks I need to know so there's some certain keywords that you're going to see that you need to recognize this going to mean exponential growth versus exponential decay so I for exponential growth of you see any kind of word problem or any kind of problem at all dealing with! that involves the words tax interest appreciate increases games anything like that that is all going to be exponential growth so you know that you were going to use this formula y equals a he's one less you're right to the X power and we're going to get today I just want to make sure that you guys know anytime you see these words tax interest appreciates increases games you're going to use this formula right here okay where is with exponential decay if you see any other way dirt bikes decrease if you lose or lose value appreciate anything that's on sale showing some kind of discount some kind of percentage off like you see a sign that says 40% off 50% off 35% off whatever the case may be like any of those things that's going to be exponential decay okay with Expedition Decay you are going to need the formula y equals a parentheses 1 - r a h please pause your screen right here I'm so that way you can write those down along with the formula that you need if not let's go ahead and jump into the next thing which is tables to exponential equations that feel like this is going to be the easiest to show you first because I feel like what the table you can kind of see where you need to start and then what the pattern is going forth from each number so there's some questions that you got to ask yourself over here so first things first is wearing where do we start will you always start at your y intercept and you're y-intercept how you find that on a table is where your ex or the X, you're going to find the number zero and whatever no where is lining up with the number 0 that is your Y intercept if you look at example one I'm going to go to my ex, I'm going to find zero and whatever number lines up with zero that is my white intercept go to is my white Intercept in my wife also known as my a okay so where I see why it was a * B to the X power right here I know that why is going to stay the same I know the ex going to stay the same but my a is now going to be my wife intercept that I just found is the number to okay so anytime you want to find your y intercepts look for the number zero on the X side on the X column even on the grass like wherever Exit Zero you know the number that goes with it is your y intercept that is where you're always going to start okay now what did you figure out where you start your next question that you need to ask is for what is my pattern what is my growth factor how much am I X every single time OK Google that's when you're going to start looking at the Y column I'm going to change color real quick that's when you start looking at the Y, so in the why I calling you got going 26 going to 18 going to 54 okay. This is different from linear because linear if you guys remember you will always add tracking every single time where is with exponential's you're always going to be multiplying every single time we're there be by a whole number or by fraction okay and when you multiply by a fraction just think of that also is the baby okay look at the Y, I've got to 61854 I got to figure out how we keep getting to this next number so two times what equals 6 I know that I'm always most always most fun 2 times what gives me 62 * 3 is going to give me 6 and I'm going to keep using that pattern to see if we get the same type of answer every single time so if I * 3 again 6 * 3 they got to give me 18 yes it does if I do 18 * 3 to take this in your calculator if you want 18 x 32 they give me 54 yes it does so I know that my growth factor I know that my pattern is 3 and you also need to know that you're growth factor represents the letter B okay so you now got your I will just talk to you now got your B which is 3 and I'm putting parentheses and then you don't know what wire asked me if you're just going to leave them the same and so when you get to deltamath I'm just finishing your assignment that is literally all they want typing a Geico is 2 * 3 or 2 parentheses 3 to the X power okay so I'm just a second it's already going to have the Y equals part written down for things that you do not have to type that in okay the only if you have to type in it is to get the parentheses put in 3 close the prince sees make sure you hit that exponent button and it should still look like this even on your Delta math calculator and then once you hit the X on the back and then you're going to type the letter X and then you can hit submit okay so all you need to do is identify where you start what's your pattern type all of that ends with the exponent button and x and you are good together okay and then what you also need to be asked selphius is your growth factor increasing or decreasing well since we're X phone number we are definitely increasing so that showing a growth okay and then what is my equation we just wrote that down okay that is it and let us all to table okay tables and turn it into an equation more time and then we're going to move on to something else so here we go so for this example once again you are going to figure out where you start what's your pattern is increasing or decreasing and from there we can write our equation okay so remember we start at our y-intercept and how you find your Y intercept is where x equal 0 so I'm going to go to my table x equals 0 and then whatever number what's up with it that is my white intercept so my y-intercept is not zero is the number that lines up with zero so that means my y-intercept is for so we're ICA it's now the number for okay look at well what's happening now with all the numbers on The Wildside what is my pattern what is happening over and over and over again when my X every single time okay I've got 16 I've got 64 and I've got 256 so I need to take your 4 * what is 16/16 * what is 6464 * what is 256 why do 4 * 4 is 16 something he going with that pattern 16 * 464 and checking on you play if you want to but 64 times for is 256 okay so I know that my pattern my growth factor my be my be is the number okay and once again I do not know where why I do not know what exit so I'm going to leave those something so when I go to put it into Delta math y equals is already going to be written for me so I do not have to put that part okay the only thing I have to put this 4 parentheses button for Clozapine make sure I hit the exponent button and then hit the letter X and then submit that's it and that's all okay let's try that again all right but this one you got 02182 32 + 3 128 okay so you want to figure out where do we start what's my growth factor my pattern is the growth factor increasing or decreasing and what is Mike waiting so I'm going to give you a second to see if you can write this one down on your own and then we'll take it together if we go all right let's go ahead and check this one together so where do we start once again that's going to be my wife y-intercept which is where x equals 0 so I'm going to find that on the chart and look for the number that goes with zero that number is too so I know that my ETA is the number to okay then I'm going to look at what is my growth factor what is my pattern have to everyday what am i x y I know my numbers are getting bigger so I know I'm increasing or I have a growth okay and I know the 2 x 4 is going to give me 8 so I'm going to keep going with that pattern to see if I get the same answer to 2 * 4 gives me 8/8 * or definitely gets me 32 and 32 times for you can check it on your calculator but it is going to give you 1:28 so your pattern or your B is the number for okay and then once again I do not know what wire exit so I'm going to just take us now and I'm going to do the same thing on Delta math y equals is already put in there for me so I do not have to write that part okay I just have to put the number to parentheses the number for Wells the parentheses make sure I hit the exponent button and then put the letter X and submit that is it and that is all okay and here is an actual example of what you would see on this matter okay so as you can see this looks exactly like your desk ask where you got your name at the top you got the title whatever sexing you're working on your dating your time stuff like that the video if you need some more help if you don't remember what I'm doing and the actual problem and know that I'm right here I kept telling you and your answer why is already written for you you do not have to take that party okay so from here we're going to do the same thing so I know them I format my formula is a times B to the X power I know that Y and X are going to stay why do actually only two things I have to do what is my AA where do I start and what is my be where am I going what's my pattern over and over okay so now with a I got to figure out where is my white intercept with my wife intercept is where it equals 0 okay where exit clear out I'm just going to go with the number that's next to it the number that's next to it is the number 5 so that is where I start to show in my Delta math box I'm going to start my answer with the number five OK Google, parentheses okay and I'm going to figure out what is my pattern what how do I get from 5 to 1515 at 4545 to 1:35 I'm going to multiply every single time by the number 3 cuz 5 * 31515 * 3 is 45 5 * 3 is 135 so in that parentheses where B is is now going to be the number three and I'm going to do the same thing make sure you hit your exponent button and then put the letter and then you can hit submit that is it and that is all four tables to exponential functions okay so now did you think I was texting there's a bunch of let's move on to the next thing which is exponential equations basics this is kind of the same thing you're just giving a word problem this time and you're going to plug in the values that you know now it's going to be a little bit different because sometimes it'll use the ABS more mad and sometimes it'll use the a parentheses 1 + r r 1 - exactly what I mean so for this one like I said all of these are going to be model just like the answer that when you guys are able to see true examples of what you're going to have on your assignment over this first one it says new car is purchased for $18,000 okay the value of the car is going to depreciate remember the free shape means that we're losing that money so that's going to be a Decay OK Google come back to that okay what kind of Decay is going to depreciate at a 13.5% interest or amount per year OK as I was wondering what is going to be the value of the car to the nearest cent after 14 years how do here but the easiest part is we can write down the formula that we need so since I know it's exponential decay I know I'm going to need y equals is going to go first and I'm going to need one minus are to the X power because any type of exponential decay is going to be 1 - are not 1 + are all right then from there I can figure out what what do I know what can I go ahead and plug it right so I know I'm not going to plug you in y or X those are going to stay the same right now I got to figure out where do I start well how much did I buy the car for I bought the car for $18,000 18000 has to go first okay and then after that I can fill in the 1 - r y I know the one in the minus sign is going to stay the same by how do I change this 13.5% to write to an actual decimal how much you have a percentage and you want to change it to a decimal you always want to scoop your decimal like I said decimal two times to the left any time you going from percent to decimal by decimal to percent percent to decimal you want a scuba to x to the left okay so I have 30 Wi-Fi okay I'm going to take this decimal I'm going to stupid once stupid twice to the left so now that's going to change 2.135 okay go ahead 13.5% I took my decimal from where it was Ice Cube do one scoop the twice to the left and now I have Point 135 so I'm going to take that point 135 and I'm going to plug it in where I see are okay now I have one minus Point 135 okay hopefully there are no questions on a part so all I do is plug in how much I pay for the car I change my percent to a decimal and plugged it in for our now the last step is to actually solve it now I can solve this because they did tell me what exit is X is always going to be your time and the time that they gave me on this problem is 14 years so we're icx now going to change that to a 14 and this is everything I'm going to put in the calculator okay so I'm going to put in 18000 parentheses 1 - 2.135 close the parentheses hit my exponent button and hit 14 okay hopefully you guys are doing this with me so that way we can come up with the same answer so 18 0 parentheses 1 - 4.135 Lowe's the parentheses exponent button and then 14 all right now I got a crazy long decimal I got another color so I got the number 2363 .18 656. Hopefully either exactly like that are very very close to that right so what this means is if I bought a car for $18,000 after 14 years and it depreciates at this 13.5% the car is only going to be worth $2,363 and some amount of cents right after 14 years now the problem is they want the value of the car to be to the nearest cent well I know sent is money and money has to decimal places okay like $5 as of two decimal places to I need some round this to two decimal places with I want around this to decimal places I got to look at the second decimal place and go to the right and hopefully in elementary school. chow chow that five or more you're going to raise the scores that means you're going to round up okay and if it's 4 or less you're going to let it rest it's the numbers going to stay the same okay so when I look at this 8 and I go to the right and I see a 6 right there that means that 18 is not going to stay at 18 it's going to rain around up to a 19 so when I put my answer into Delta math I'm going to keep the 2363 the same but that money that sent part is not going to stay 18 is now 19 so now it's $2,363.19 and then I will hit the men and it would tell me that is correct okay I know that was a lot with practice I promise you you'll get it okay so we're going to try another one on the next thing that I have and then if you have any questions feel free to talk to me or any of your teachers and they can definitely explain this one again okay here we go alright so we're a nudist try this again so we got $6,700 is placed in an account with an annual interest rate of 8.25% so how much would the account how much will be in the account after 28 years to the nearest S&R members is money that's going to be two decimal places okay alright then I know that is going to have an interest rate interest means you add on some extra money you get some extra money okay so interest rate is always going to be some kind of grow so I know what I'm going to have a growth I need y equals a parentheses 1 + r to the X power okay that's going to be my growth that I need to plug in what we know once again okay hey hey it's going to be where you start we don't know what y equals 2 that's our total so why is going to stay the same day is the amount that we start with in this account which is $6,700 to 6700 is going to go right here cuz that's where I start with I'm going to keep the one in the plus sign in the same but now I got to figure out my rate to 5%, remember if your changing from a person duodecimo you got a stupid 2 times to the left okay to take that decimal that you got cuz I've got 8.25% take that Decima stupid stupid twice ears where the decimal is now anytime you have a blank right here you just place it with the zero okay so now this changes from 8.25% 2.082 and that's going to go where are is so now I have one plus 2008 25 then X remember is your time and we want to know how much is going to be in the account after 28 years so ask now the number 28 okay so now I'm literally going to take all that I just wrote and blue so 6700 parentheses 1 + 08 25 going to hit the exponent button and then 28th and we're going to see what answer we get and we got that we've got 6700 parentheses 1 + point zero eight two five closer parentheses at the exponent button it's 28 hit answer and I'm going to get something crazy like +61-661-667-4471 73 the nearest so I just need two decimal places remember you got 47 but you got to take this time to go look to the right number five or more Rays at school around it up if it's for Less let it rest but it stay the same so since it's the one that 47 is going to stay up 47 so my amount yes $61,667.47 that's how much will be in the account after 28 years okay then I'll just hit submit and then I'm like I said if you need more help ask me then we'll be glad to explain it to you otherwise I'm going to go to the next part which is matching exponential equations to the context okay so this is where I give you like a word problem or scenario and then you just match how to set up the actual equation okay and so once again this to be Weigel's a b to the x or this could be why it was a parentheses OnePlus Two the x or y Hue Bridge C1 - architect it could be three different ways that you can see it but we're going to try to give you all the way so that way you got somebody confused all right you got a group consisting of 30 aggressive. and they're going to double in size every single hour and so you just want to know which equation matches the number of zombies after 8 hours well we know that if it's going to double in size every hour double means you're going to multiply okay so you're the most about you every single time and you know where you start going to start with 30 zombie okay so looks like we're going to be using white with a parentheses B to the X power okay you got your starting place got the girls back there and then you got your ex or your time right so why is going to stay the same cuz that's our total we don't know yet right I guess in this case is really easy for zombies cuz we don't know how right we do know that we're going to start with $30 we know that they're going to double so we got a x 2 and we want to know how many zombies are we going to have after 8 hours so that X is going to change to a 8 x is your time okay I just got to find this answer and then I'm done well that answers right here it's see so I would click it and then click submit and then I'm done okay so just find out where you start figure out what you're multiplying by and then we got to have any time so that way you could change your ex to that and your good okay the next one is Diandra has a collection of vintage action figures that's worth $250 okay she ate Mundelein that appreciates at a rate of 16% per year which equation represents the value of collection of the collection after 8 years ok right so that means go to represent a growth so I'm going to have y equals a parentheses 1 + r to the X power all right now here we go all right. Got y equals 8 vs OnePlus R to the X power so what's going to happen is I am going to plug in what I know why I know I got to start with 250 so I have y equals 250 that doesn't eliminate anything yet then one plus I is going to stay the same okay now my rate is 16% and we just changed it to a decimal just a minute I'm going to do the same thing again alright see you take your percentage you got to find your desk now your decimal is going to be in this time cuz you don't see it so 16 is like 16.0 so you're going to take that at the end you're going to stupid twice twice and now you should have okay dad is going to go where the art is all right now I have one plus your points now I got to know the value of the escalation after 8 years so where the exit is we're now we're going to plug in at 8 so once you plug in all this stuff all you got to do is find it on the lips so that's going to be be I would just click that if I was on computer and imma get it right ok and we can move on to the next month so here we go all right here's a Darwin I want you to try for a second and then we'll check it yeah there I'm trying to find my switch so I can pause the screen it's not working okay so since my switch is not working I guess I'll go ahead is one with y'all or $22,500 the value of the car depreciates at a rate of 6% per year because I'm underlined appreciates cuz we need that word and then we need to know which equation represents the value of the car after two years okay so since we know the car is going to depreciate or lose value is not going to be worth that much money that mean this going to be an exponential decay the one you have exponential decay you're going to have y equals a parentheses 1 - R to the X power and then you just plug-in what you know your  is going to be where you start all right so are you going to be how much you you bought the car for which is going to be $22,500 the one in the minus sign are going to stay the same now let's talk about the rate would you just sit right here remember if you do not see the decimal the decimals after the last number right now I've got this sticks I've got this decimal after the 6 and I've got a stupid once stupid twice to the left and where there's a blank I'm going to plug in a 05 so now that 6% just changed you point zero six and that is going to go where are you is so 1 - 4.06 and then my time is the back of the car for two years so exit now too so now I'm start with and look for this answer over here on the side so I need $22,500 click it if I was on the computer right now I would hit them it and I'm going to get it right okay I think that is the last time I have yes so we are at the end of this video like I said if you have any questions feel free to ask me ask any of your teachers kotar doctor Parish Miss Gately Miss Nelson whoever and we will be more than happy to help you until next time please get your work done turn it in on time and if you need anything just let us know all right donkey lock the next time I'll see y'all later bye

Uploaded by Kristen Harris.

Videos

Exponential Functions - Delta Math Help

More videos from Kristen Harris