Use the fact that 14 years after 1982 the population increased by 10 million to find k to three decimal places.

Question

17) The population of a particular country was 23 million in 1982; in 1996, it was 33 million. The

exponential growth function A =23e

kt describes the population of this country t years after 1982.

Use the fact that 14 years after 1982 the population increased by 10 million to find k to three

decimal places.

A) 0.164 B) 0.474 C) 0.036 D) 0.026

Answer 1

P(t)=23e^kt

where P(t) is the population t years after 1982, 23 (million) is the population in 1982, t is years since 1982, and k is a constant to be determined. 14 years after 1982 (t = 14), the population increases by 10 million, so P(14) = 23+10 = 33 million.

33 = 23e^14k

33/23 = e^14k

ln(33/23) = 14k

ln(33/23)/14 = k

Use your calculator to get the answer. Round to three decimal places.