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

Step-by-step 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,

$\frac{5508}{4636}=\frac{Ae^{2018B} }{Ae^{2008B} }$

$e^{10B}=\frac{5508}{4636}$

$10B=ln(\frac{5508}{4636} )=0.17235$

$B=0.017235$

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