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?

Question

Cheyenne Pennington

Mathematics

9 May, 16:12

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?

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Davian Booth · Answer 1

The formula for an exponential growth rate is in the form of:

P = Po e^ (r t)

Where,

P = final population after how many years = 8 500

Po = the initial population = 5 000

r = the growth rate = unknown (the variable we have to find for)

t = time in years = 4 years

Rewriting the equation in the form to find for r:

P / Po = e^ (r t)

ln (P / Po) = r t

r = ln (P / Po) / t

r = ln (8500/5000) / 4

r = 0.1327 / year

Therefore the growth rate is about 13.27% per year.