Question

After a devastating winter, when thousands of fish died, an environmental scientist has replenished the trout stock in a fishing pond. He started with 5,000 baby trout and has finished a count to find that, in 4 years, the population is estimated to be 8,500. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new trout population?

Answer 1

The annual growth rate of the new trout population is approximately 12.0%.

Step-by-step explanation:

To find the annual growth rate of the trout population, we can use the exponential growth formula:

P = P0ert

where P is the final population, P0 is the initial population, r is the annual growth rate, and t is the number of years.

In this case, we have P = 8,500, P0 = 5,000, and t = 4. Plugging these values into the formula, we can solve for r:

8,500 = 5,000e4r

Divide both sides by 5,000:

1.7 = e4r

Take the natural logarithm of both sides:

ln(1.7) = 4r

Divide both sides by 4:

r ≈ ln(1.7)/4 ≈ 0.120