Answer to Question #306554 in Algebra for carleek

Question

A town has a population of 15000 and grows at 4.5% every year. To the nearest year, how long will it be until the population will reach 35900?

Answer 1

The exponential growth rate is given by:

P(x) = a(1+r)^x

where

P(x) = the population exponential growth function

a = initial population at x=0

r = growth rate

x = number of time intervals in years

Given the population after x years P(x) = 35,900

a = 15,000

r=4.5% = 0.045

We replace the values in the equation and solve for x:

35,900 = 15,000(1+0.045)^x divide through by 15,000

(35,900/15,000) = (1.045)^x

2.39 = (1.045)^x Introduce logarithms on both sides

log(2.39) = xlog(1.045)

x = log(2.39)/log(1.045)

x = 19.8

Which is approximately equal to 20 years

Answer: 20 years