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suppose the population of a town is growing exponentially. the population was 4,636 in 2008 and grew to 5,508 in 2018. what is the approximate growth rate of the population?

1 Answer

5 votes

94.93

Explanation:

The standard equation used to model a exponential growth is given by
f(t)=Ae^(Bt)

Given two data points, which are both explicitly a function of time, it is easy to solve the two equations,


4636=Ae^(2008B) ,5508=Ae^(2018B)

Dividing the second equation by the first,


(5508)/(4636)=(Ae^(2018B) )/(Ae^(2008B) )


e^(10B)=(5508)/(4636)


10B=ln((5508)/(4636) )=0.17235


B=0.017235

Substituting in first equation,
A=4.32645\textrm{x}10^(-12)

Growth model :
f(t)=(4.3265\textrm{x}10^(-12) )e^(0.017235t)

Growth rate=
ABe^(Bt)=
94.93

∴Approximate growth rate as of 2018 = 95

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