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The function [tex]$f(x)=32(1.5)^x$[/tex] represents the chipmunk population of a forest [tex]$x$[/tex] years after it was first studied. What was the original population of chipmunks?

A. 72
B. 32
C. 48
D. 21

Sagot :

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.