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QuizMultiple Choice

Exponential Decay Functions

Question 2 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P

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
A
f(x) = 1,200(1.03)x
B
f(x) = 1,200(0.03)x
C
f(x) = 1,200(0.97)x
D
f(x) = 1,200(0.97x)

Explanation

A population that decreases by 3% each year retains 100% − 3% = 97% of its size each year, so the yearly multiplier is 0.97. Starting with 1,200 frogs, the population after x years is f(x) = 1,200(0.97)^x. Therefore, choice C is correct.

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