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:

$$\text{There will be }904021\text{ rabbits.}$$