Question
A deer population in a forest starts with 100 and increases by 9% each year. Write an exponential function that models the data
Answers
GPT-4o mini
To model the growth of the deer population using an exponential function, we can use the general formula for exponential growth:
\[
P(t) = P_0 \cdot (1 + r)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years.
In this case:
- The initial population \( P_0 \) is 100.
- The growth rate \( r \) for 9% is 0.09.
Substituting these values into the formula, we get:
\[
P(t) = 100 \cdot (1 + 0.09)^t
\]
which simplifies to:
\[
P(t) = 100 \cdot (1.09)^t
\]
This function \( P(t) \) models the deer population after \( t \) years.
\[
P(t) = P_0 \cdot (1 + r)^t
\]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years.
In this case:
- The initial population \( P_0 \) is 100.
- The growth rate \( r \) for 9% is 0.09.
Substituting these values into the formula, we get:
\[
P(t) = 100 \cdot (1 + 0.09)^t
\]
which simplifies to:
\[
P(t) = 100 \cdot (1.09)^t
\]
This function \( P(t) \) models the deer population after \( t \) years.