Question

a native wolf species has been reintroduced into yellowstone national park and grows according to the law of exponential growth. originally 200 wolves were transplanted. after 3 years, the population had grown to 270 wolves. what is the growth rate?

Answer 1

The growth rate of the reintroduced wolf population in Yellowstone National Park after 3 years is approximately 4.92% per year.

Step-by-step explanation:

To find the growth rate of the wolf population in Yellowstone National Park that follows exponential growth, we can use the formula P(t) = P₀ert, where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and e is the base of the natural logarithm.

In this scenario, the initial population P₀ is 200 wolves, the population after 3 years P(3) is 270 wolves, and t is 3 years. We need to solve for r.

First, divide both sides of the equation by P₀:
270 / 200 = e3r. This simplifies to 1.35 = e3r.

Next, take the natural logarithm of both sides to solve for r:
ln(1.35) = 3r. Then, r = ln(1.35) / 3.

Using a calculator, r ≈ 0.0492 or about 4.92% per year.