To determine the original population of chipmunks, we need to evaluate the function [tex]\( f(x) = 32(1.5)^x \)[/tex] when [tex]\( x = 0 \)[/tex]. This represents the population at the time the forest was first studied.
Let's substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 32 (1.5)^0
\][/tex]
We know that any number raised to the power of 0 equals 1. Therefore:
[tex]\[
(1.5)^0 = 1
\][/tex]
Substituting this back into the function:
[tex]\[
f(0) = 32 \cdot 1 = 32
\][/tex]
So, the original population of chipmunks is:
[tex]\[
\boxed{32}
\][/tex]
Therefore, the correct answer is B.
