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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?

Verified Answer :

caylus

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:

\(y = 1200(0.97)^x\)

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 \(y = 1200(0.97)^x\)

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