Environmentalists estimate an annual population decrease of giraffes in the wild of 3.5% due to development. This can be modeled by the function p(x) = 140,000(0.965)x, where x is the number of years of tracking the populations. Conservationists have developed a sanctuary that has shown the ability to increase the population by 0.85% per year. The increase can be modeled by the function S(p) = p(1.0085)x.
Answer
A
S(p(x)) = 135,100(0.9732)x
B
S(p(x)) = 135,100(1.9735)x
C
S(p(x)) = 140,000(0.9732)x
D
S(p(x)) = 140,000(1.9735)x
Explanation
Substitute p(x) into the sanctuary model: S(p(x)) = 140,000(0.965)^x(1.0085)^x. Combine the factors raised to the same power: 0.965 × 1.0085 = 0.9732025, which rounds to 0.9732. So the model is 140,000(0.9732)^x, choice C.
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