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After years of overhunting, environmental scientists have reintroduced bears to Yellowstone National Park. The initial number of bears reintroduced to the park was 20 and, after 10 years, the population is estimated to be around 110.

Part A: Assuming an exponential growth pattern, use the information given to write the model for this situation.

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.

Part B: What is the annual growth rate (rounded to the nearest tenth of a percent) of the new bear 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 22, 2016
 #1
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+5

A(t) = A0(1 + r)t

110  = 20(1 + r)10

Divide by 20:   5.5  = (1 + r)10

Take the 10th root of both sides:  1.1859  =  1 + r

Subtract 1 from both sides:  r  = 0.1859  or about 18.6%

 Feb 22, 2016

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