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?

Hello,

[tex] x_{0}=1200[/tex]

[tex] x_{1}=\frac{97}{100}*1200[/tex]

[tex] x_{2}=(\frac{97}{100})^2*1200[/tex]

[tex] x_{3}=(\frac{97}{100})^3*1200[/tex]
...
[tex] x_{n}=(\frac{97}{100})^{n}*1200[/tex]

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wifilethbridge wifilethbridge · Answer 2 · 2019-06-25T07:58:44+02:00

Answer:

[tex]y = 1200(0.97)^x[/tex]

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 : [tex]y = a(1-r)^n[/tex]

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:

[tex]y = 1200(1-0.03)^x[/tex]

[tex]y = 1200(0.97)^x[/tex]

Hence function represents the frog population after x years is [tex]y = 1200(0.97)^x[/tex]