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5. Write an exponential function for each situation a. Apopulation of 250,000 increases by 5 % each year. b. An item costs$45, and the price drops by 3 % each year....

Question

5. Write an exponential function for each situation a. Apopulation of 250,000 increases by 5 % each year. b. An item costs$45, and the price drops by 3 % each year.

5. Write an exponential function for each situation a. A population of 250,000 increases by 5 % each year. b. An item costs $45, and the price drops by 3 % each year.



Answers

Write an exponential function to
model the situation. Tell what each variable represents. A population of 310,000 increases by 15% each year.

We're gonna write on the exponential function. Where the situation where the concert attendance of 10,000 increasing 5% each year. Greater exponential model. We're gonna follow the form. Why? Equal C times one plus R to the T power. So why is gonna represent our attendance? C is going to represent our initial or tenants. Are is going to represent our row three and we're gonna write this as a decimal. T was gonna represent time in years. So we're gonna follow the model. Why? He will see times one plus R to the power. So why is gonna equal our initial attendance with 10,000? We're gonna multiply that by one plus. So our is our growth rate. 5%. We gonna change up to a decimal. So we're gonna move that decimal 0.2 to the left. So that's gonna be 0.5 We're gonna raise that to the T power, and this is an exponential model. There are concert attendance

Okay, so when we're dealing with exponential growth, another common type of application is going to be population growth because population growth can either double or increase over time. I see here that since I'm multiplying by 1.14 each year, since it's greater than one, I know this is going to be exponential growth And I'm starting at 12,400 people. Okay with tea in years. So let's find the population of the town after three years. Okay, Since T. Is measured in years, we're just going to plug it in when T equals three. So it's if I were to plug in three into this formula, right? And I were applying the same Growth 1.14 to the 3rd. How many? Um What would I have after three years? Well I would have approximately 18371. It says it find to the nearest 100. So this is um to the nearest hundreds place. This is about this seven will round up that three. So about 18,400 people will be in this town after three years at this growth rate. Now, let's say I want to figure it out after 4.25 years. So this is really after um for in a quarter year, so maybe um couple months. So I'm still going to plug this into this formula. Considering everything else is the same 4.25 Hard to plug this into my formula in my calculator, I would get approximately 21006 40. Okay, I'm running to the nearest hundreds place. Does this four round up at six, Nope. So it'll be about approximately 21,600 people in the town after a little more time has passed.

So an exponential model. It is defined by the equation. A equals a sub zero times two to the power of cheese about of I D and a sub zero is the initial population and deice the doubling time. And so because we're given that a subzero is 5000 and the doubling time is three, we can go ahead and plug in these values and to our known equation. So a is equal to 5000 times two to the power of T divided by three.

In this problem, we need to write an exponential equation describing the situation that we have an initial population. Let's call it be not that is 200 and it doubles so Piece of two equals five months, so it doubles every five months. Now. The general formula for a population that doubles every D sub two months is BFT equals be. Not times. He's up to raised to the power. Mhm. All right. Great. Not that he's up to here. There's a do here. So Times T Sub two. Mt. So this gives our Population as a function of time as 200 times two Raised to the Power five T. And that is a required equation where T is in months where D. Is the time in months, The time in months.


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