Question

the function $f(x) = 40(1.2)^x$ represents the fox population of a forest $x$ years after it was first studied. what was the original population of the foxes?
a. 58
b. 40
c. 33
d. 48

Explanation:

Step1: Identify the original time

The original population is when \( x = 0 \) (at the start of the study).

Step2: Substitute \( x = 0 \) into the function

For the function \( f(x)=40(1.2)^{x} \), when \( x = 0 \), we use the property of exponents that \( a^{0}=1 \) (where \( a
eq0 \)). So \( (1.2)^{0}=1 \).
Then \( f(0)=40\times(1.2)^{0}=40\times1 = 40 \).

Answer:

B. 40