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)=(97)/(100)*1200`


`x_(2)=((97)/(100))^2*1200`


`x_(3)=((97)/(100))^3*1200`
...

`x_(n)=((97)/(100))^(n)*1200`

Answer 2

`y = 1200(0.97)^x`

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`