Question

7 Question Category Exponential Growth

Select the correct answer
A country's population in 1993 was 183 million. In 2001 it was 187 million. Estimate the population in 2004 using the exponential growth formula Round your answer to the nearest million

Answer 1

189 million

Explanation:

The exponential formula can be written from the given information. We are given a growth factor of 187/183 that applies to an 8-year time period. That means we need to scale the time by a factor of 8 if we're going to use that growth factor:

p = a·b^t . . . . . . . initial value 'a'; growth factor b

p = 183(187/183)^(t/8) . . . . where t is years after 1993

For 2004, 11 years after 1993, the estimated population is ...

p = 183(187/183)^(11/8) ≈ 189 . . . million

The population estimate for 2004 is 189 million.

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Additional comment

The annual growth factor is (187/183)^(1/8) ≈ 1.00271. That is, it is about 0.271% per year.