Question

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?

Answer 1

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