Question

13 mark for review $f(x)=3,000(0.75)^{x}$ a conservation scientist implemented a program to reduce the population of a certain species in an area. the given function estimates this species population $x$ years after 2008, where $xleq8$. which of the following is the best interpretation of 3,000 in this context? a the estimated percent decrease in the population for this species and area every 8 years after 2008 b the estimated percent decrease in the population for this species and area each year after 2008 c the estimated population for this species and area 8 years after 2008 d the estimated initial population for this species and area in 2008

Explanation:

The general form of an exponential - decay function is $y = a(1 - r)^x$, where $a$ is the initial amount, $r$ is the rate of decay, and $x$ is the number of time - periods. In the function $f(x)=3000(0.75)^x$, when $x = 0$ (corresponding to the year 2008), $f(0)=3000(0.75)^0=3000$. So, 3000 represents the initial value of the population in 2008.

Answer:

D. The estimated initial population for this species and area in 2008