Question

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?

Answer 1

Hello,

$x_{0}=1200$

$x_{1}=\frac{97}{100}*1200$

$x_{2}=(\frac{97}{100})^2*1200$

$x_{3}=(\frac{97}{100})^3*1200$
...
$x_{n}=(\frac{97}{100})^{n}*1200$

Answer 2

Answer:

$y = 1200(0.97)^x$

Step-by-step explanation:

Ginny determines that the population is decreasing at an average rate of 3% per year.

So, this is an exponential decay case

Formula : $y = a(1-r)^n$

where a is the amount after n years

a is the initial amount

r is the rate of depreciate

n is the number of years

Now we are given that When she began her study, the frog population was estimated at 1,200.

So, a=1200

r = 3% = 0.03

n =x

Substitute the values in the formula:

$y = 1200(1-0.03)^x$

$y = 1200(0.97)^x$

Hence function represents the frog population after x years is $y = 1200(0.97)^x$