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:

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