Question

the function $f(x) = 68(1.3)^x$ represents the possible squirrel population in a park $x$ years from now. each year, the expected number of squirrels is ____ the number the year before. \
\
a. 1.3 times \
b. 0.3 times \
c. 3 times \
d. 3 more than

Explanation:

Step1: Recall exponential function form

The general form of an exponential growth function is \( f(x)=a(b)^x \), where \( a \) is the initial amount, \( b \) is the growth factor, and \( x \) is the time variable. If \( b > 1 \), it represents growth, and the amount each time period is \( b \) times the previous amount.

Step2: Analyze the given function

The given function is \( f(x) = 68(1.3)^x \). Comparing it to the general exponential form \( f(x)=a(b)^x \), we can see that \( a = 68 \) (initial squirrel population) and \( b = 1.3 \) (the growth factor).

This means that for each increase in \( x \) (each year), the population is multiplied by \( 1.3 \). So each year, the expected number of squirrels is \( 1.3 \) times the number the year before.

Answer:

A. 1.3 times