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. assume the growth rate is 10.52%. if this trend continues, how many wolves will there be in 10 years?

Answer 1

To predict the wolf population in Yellowstone after 10 years with a consistent growth rate of 10.52%, we use the exponential growth formula, applying the given initial population and growth rate to solve for the future population.

Step-by-step explanation:

The question asks about exponential growth, specifically pertaining to the growth of a reintroduced wolf population in Yellowstone National Park. To calculate the future population of wolves from an initial population under exponential growth, we use the formula:

P(t) = P0 × e(r×t)

Where P(t) is the future population after time t, P0 is the initial population, r is the growth rate, and e is the base of the natural logarithm. Assuming the growth rate is consistent at 10.52% and using the given initial population of 200 wolves, we can calculate the expected population after 10 years:

P(10) = 200 × e(0.1052×10)

After solving for P(10), we can determine how many wolves are expected to be in Yellowstone after 10 years given the current growth trend.