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%

Question

Mathematics

Pranav Decker

17 August, 17:29

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%

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Hanson · 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%