Question

The function f(x) = 50(0.952)x, where x is the time in years, models a declining feral cat population. How many feral cats will there be in 9 years?

Answer 1

Answer: B) 32

Work Shown:

f(x) = 50(0.952)^x

f(9) = 50(0.952)^9

f(9) = 32.1146016801717

f(9) = 32 approximately

Side note: the exponential function is in the form a*b^x with b = 1+r = 0.952, which solves to r = -0.048. The negative r value means we have a 4.8% decrease each year.

Another note: you don't even need to use math to answer this question. Note how 50 is the starting population and the population is declining. Only choice B has a value smaller than 50, so we can rule out the others right away.

Answer 2

32

Explanation:

The initial value of the population is f(0) = 50(0.952^0) = 50. If the population is declining, it must be less than 50 in 9 years. The only answer choice that is less than 50 is ...

about 32 feral cats

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You can evaluate f(9) to choose the same answer:

f(9) = 50(0.952^9) ≈ 32.114 ≈ 32