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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?


f(x) = 1,200(1.03)x

f(x) = 1,200(0.03)x

f(x) = 1,200(0.97)x

f(x) = 1,200(0.97)x

Verified Answer :

Answer:

f(x) = 1,200 * (0.97)ˣ

Step-by-step explanation:

MrRoyal

The population of the frogs in x years is (c) \(f(x) = 1200(0.97)^x\)

The initial population of the frogs is given as:

\(a =1200\)

The decay rate is given as:

\(r = 3\%\)

An exponential function that for decay is represented as:

\(f(x) = a(1 - r)^x\)

Substitute values for (a) and r

\(f(x) = 1200(1 - 3\%)^x\)

Express percentage as decimal

\(f(x) = 1200(1 - 0.03)^x\)

Add 1 and 0.03

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

Hence, the population of the frogs in x years is (c) \(f(x) = 1200(0.97)^x\)

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