Question

a population of squirrels is growing in a louisiana forest with a monthly growth constant of 30 percent. if the initial count is 100 squirrels, how many are there in a year? round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number.

Explanation:

Identify the given parameters

We are given:

• Initial population \(P_0 = 100\) squirrels.
• Monthly growth constant \(r = 30\% = 0.30\).
• Time period \(t = 1\) year, which corresponds to \(12\) months since the growth rate is monthly.

Set up the exponential growth model

The population \(P(t)\) after \(t\) months is modeled by the continuous exponential growth formula:

$$P(t) = P_0 e^{rt}$$

Calculate the population after one year

Substitute \(P_0 = 100\), \(r = 0.30\), and \(t = 12\) into the formula:

$$P(12) = 100 e^{0.30 \times 12}$$

$$P(12) = 100 e^{3.6}$$

Compute the numerical value

First, calculate the exponential term to at least six decimal places:

$$e^{3.6} \approx 36.598234$$

Now, multiply by the initial population:

$$P(12) \approx 100 \times 36.598234 = 3659.8234$$

Round to the nearest whole number

Rounding \(3659.8234\) to the nearest whole number gives:

$$P(12) \approx 3660$$

Answer:

A population of squirrels is growing in a Louisiana forest with a monthly growth constant of 30 percent. If the initial count is 100 squirrels, how many are there in a year? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number.

<blank>3660</blank> squirrels