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After years of overhunting, environmental scientists have reintroduced elk to Yellowstone National Park. The initial number of elk reintroduced to the park was 230 and, after 8 years, the population is estimated to be around 595. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new elk population in Yellowstone National Park?

Hint: A(t) = A0(1 + r)^t, where A(t) is the final amount, A0 is the initial amount, r is the growth rate expressed as a decimal amount, and t is time.

 Feb 11, 2016
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595 = 230 (1 + r)^8      divide both sides by 230

 

595/230  = (1 + r)^8     take the 8th root of both sides

 

1.126 = 1 + r      subtract 1 from both sides

 

.126  = r  = about 12.6%

 

 

 

cool cool cool

 Feb 11, 2016

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