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Albertrami9019
07.10.2019 •
Mathematics
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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Ответ:
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.
Ответ: