Question

A native wolf species has been reintroduced into a national forest. Originally, 46 wolves were transplanted. Assuming that the population is growing exponentially at a rate of 5.6%, how long will it take for the population to reach 150 wolves? Round your answer to the first decimal place.

Answer 1

To solve this problem, we can use the exponential growth formula:

Nt = N0 × (1 + r)^t

where Nt is the population at time t, N0 is the initial population, r is the growth rate, and t is the time.

In this case, N0 = 46, r = 0.056 (since the growth rate is given as a percentage, we need to divide by 100 to get the decimal equivalent), and we want to find t when Nt = 150. So we can plug in these values and solve for t:

150 = 46 × (1 + 0.056)^t

Divide both sides by 46:

150/46 = (1 + 0.056)^t

Take the natural log of both sides:

ln(150/46) = t × ln(1 + 0.056)

Solve for t:

t = ln(150/46) / ln(1 + 0.056) ≈ 8.6 years

Therefore, it will take approximately 8.6 years for the wolf population to reach 150 individuals.