Question

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. which function represents s(p(x)), rounded to the nearest ten - thousandth? s(p(x)) = 135100(1.9735)^x s(p(x)) = 140000(0.9732)^x

Explanation:

Step1: Substitute $p(x)$ into $S(p)$

We know $p(x)=140000(0.965)^x$ and $S(p)=p(1.0085)^x$. Substitute $p(x)$ into $S(p)$:
\[S(p(x)) = 140000(0.965)^x\times(1.0085)^x\]

Step2: Use the exponent - rule $a^m\times b^m=(a\times b)^m$

\[S(p(x))=140000\times(0.965\times1.0085)^x\]
Calculate $0.965\times1.0085 = 0.9732025\approx0.9732$
So $S(p(x)) = 140000(0.9732)^x$

Answer:

$S(p(x)) = 140000(0.9732)^x$