Question
A population of squirrels in a certain region doubles every month.
Which function can be used to find the number of squirrels at the end of m months if there are initially 84 squirrels?
Which function can be used to find the number of squirrels at the end of m months if there are initially 84 squirrels?
Answers
GPT-4o mini
To model the growth of the squirrel population, we can use an exponential growth function. Since the population doubles every month, we can express the number of squirrels after \( m \) months with the following function:
\[
P(m) = P_0 \cdot 2^m
\]
where:
- \( P(m) \) is the population after \( m \) months,
- \( P_0 \) is the initial population (which is 84 squirrels in this case),
- \( m \) is the number of months.
Plugging in the initial population:
\[
P(m) = 84 \cdot 2^m
\]
Thus, the function to find the number of squirrels at the end of \( m \) months is:
\[
P(m) = 84 \cdot 2^m
\]
\[
P(m) = P_0 \cdot 2^m
\]
where:
- \( P(m) \) is the population after \( m \) months,
- \( P_0 \) is the initial population (which is 84 squirrels in this case),
- \( m \) is the number of months.
Plugging in the initial population:
\[
P(m) = 84 \cdot 2^m
\]
Thus, the function to find the number of squirrels at the end of \( m \) months is:
\[
P(m) = 84 \cdot 2^m
\]