Answer:
(b)962.18 square km
Explanation:
Given the function:
[tex]f(A)=-7.5+204.9\ln (A)[/tex]
The graph of the function is given below:
(b) To determine f^-1(1400), find the value of A at which f(A)=1400.
[tex]\begin{gathered} f(A)=-7.5+204.9\ln (A)=1400 \\ 204.9\ln (A)=1400+7.5 \\ 204.9\ln (A)=1407.5 \\ \ln (A)=\frac{1407.5}{204.9} \\ A=\exp (\frac{1407.5}{204.9})^{} \\ A\approx962.18 \\ \implies f^{-1}(1400)=962.18\operatorname{km}^2 \end{gathered}[/tex]
(c)
In order for the number of species on the island to be 1400, the area of the island must be approximately 962.18 square km.
