The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Approximately when will the population reach 1 million?

Question

Deanna Frank

Mathematics

6 November, 08:18

The population of Knoxville is 500,000 and is increasing at the rate of 3.75% each year. Approximately when will the population reach 1 million?

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Answers (1)

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Magdalena Hess · Answer 1

Dp/dt =.0375 people/year

ln p =.0375 t + c

p = c e^ (.0375 t)

when t = 0, p = 500,000

so

p = 500,000 e^ (.0375 t)

so

2 = 1,000,000/500,000 = e^ (.0375 t)

ln 2 =.0375 t

t = 18.5 years