In 2012, the population of a city was 5.31 million. The exponential growth rate

Question

In 2012, the population of a city was 5.31 million. The exponential growth rate was 1.44% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 88 million? d) Find the doubling time. a) The exponential growth function is P(t)equals= nothing, where t is in terms of the number of years since 2012 and P(t) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Explanation / Answer

We have to use the following formula

P(t)=P0 ekt

k=1.44%=.0144

a. P(t)= 5.31 e.0144 t

b. P(t)=5.31 e.0144*6= 5.79 million

c. 88=5.31 e.0144t

88/5.31=e.0144t

Taking ln on both sides

ln(88/5.31)=.0144 t

t=195 years

d. 10.62=5.31 e.0144t

t=48.1 years

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