The population of a southern city follows the exponential If

The population of a southern city follows the exponential If the population doubted in size over 30 months and the current population a 90.000. what will the population be 3 years from now? What will the population be 3 years from now? the population will be approximately people.

Solution

generalexponential growth equation is N=N₀e^kt ,here t in months

current population N₀=90000

given population doubles in 30 months

N=180000

180000=90000e^k*30

e^k*30=2

30k=ln2

k=(1/30)ln2

k=0.0231

N=90000e^0.0231t

3 years from now, t=3*12=36 months

N=90000e^0.0231*36

N=206729

population will be approximately 206729 people