Question

The number of rabbits present in a community can be modeled by a function, where P(t)=500e0.5t is the number of rabbits present after t years. Using this model, determine how many rabbits will be present after 15 years, rounding to the nearest rabbit.(1 point) After 15 years, there will be rabbits.

Answer 1

To find the number of rabbits present after 15 years using the given function \( P(t) = 500e^{0.5t} \), we need to substitute \( t = 15 \) into the function.

\[
P(15) = 500e^{0.5 \times 15}
\]

Calculating \( 0.5 \times 15 \):

\[
0.5 \times 15 = 7.5
\]

Now substituting back into the function:

\[
P(15) = 500e^{7.5}
\]

Next, we need to calculate \( e^{7.5} \). Using a calculator, we find:

\[
e^{7.5} \approx 1808.042
\]

Now we calculate \( P(15) \):

\[
P(15) = 500 \times 1808.042 \approx 904021
\]

Rounding to the nearest rabbit, the number of rabbits present after 15 years will be:

\[
\text{There will be } 904021 \text{ rabbits.}
\]