Question

scientists released 8 rabbits into a new habitat in year 0. each year, there were twice as many rabbits as the year before. how many rabbits were there after x years? write a function to represent this scenario. a. $f(x)=8(2)^x$ b. $f(x)=2(8)^x$ c. $f(x)=8(x)^2$ d. $f(x)=2(x)^8$

Explanation:

Step1: Identify the type of growth

This is an exponential growth problem. The general form of an exponential function is $f(x) = a(b)^x$, where $a$ is the initial amount, $b$ is the growth factor, and $x$ is the time.

Step2: Determine the initial amount ($a$)

In year 0, the number of rabbits is 8. So, $a = 8$.

Step3: Determine the growth factor ($b$)

Each year, the number of rabbits is twice as many as the year before. So, the growth factor $b = 2$.

Step4: Write the function

Substituting $a = 8$ and $b = 2$ into the exponential function formula, we get $f(x) = 8(2)^x$.

Answer:

A. $f(x) = 8(2)^x$