The number of rabbits present in a community can be modeled by a function, where P(t)=500e0.5t

Question

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 model \( P(t) = 500e^{0.5t} \), we need to substitute \( t = 15 \) into the function.

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

Calculating \( 0.5 \cdot 15 \):

\[ 0.5 \cdot 15 = 7.5 \]

Now, substituting back into the equation:

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

Next, we need to calculate \( e^{7.5} \):

\[ e^{7.5} \approx 178.879 \]

Now we can multiply:

\[ P(15) = 500 \cdot 178.879 \approx 89439.5 \]

Rounding to the nearest rabbit, we get:

\[ P(15) \approx 89440 \]

Thus, after 15 years, there will be approximately 89440 rabbits.