Answer to Question #159533 in Algebra for Leighanna

Question

A town has a population of 14000 and grows at 2.5% every year. What will be the population after 5 years, to the nearest whole number?

Answer 1

initial population = 14000

growth rate = 2.5% every year

so after one year population is = 14000+14000(2.5/100) = 14350

after 2 year population is = 14350+14350(2.5/100) = 14709

this will continue till 5 years so reduce it in a formula as

$pop(n)= pop(initial) *(1+\frac{rate per year}{100})^n$

where,

pop(n) = population after n years.

pop(initial) = initial population.

n = number of years

so, population after n years with growth rate 2.5% is

$pop(5) = 14000(1+\frac{2.5}{100})^5$

$pop(5) = 14000(1.025)^5$

pop(5) = 15839.74

thus, population after 5 years is 15840.