Question

The population of a city is growing according to the exponential model P = Ce^kt, where P is the population in thousands and t is measures in years. If the population doubles every 11 years what is k, the city's growth rate? Round answer to the nearest hundredth. A) 2.8% B) 4.4% C) 6.3% D) 8.9%

Answer 1

P = Ce^kt ( P = 2C & t=11 years, given)

2C = Ce^kt ==> 2C = Ce^(11k) ==> 2 = e^(11k)
ln(2) = 11klne ==> ln(2) = 11k ==> 0.693147 = 11k ===> k= 0.0630 or 6.3%