The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation mc024-1.jpg represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.

QUESTION POSTED AT 01/06/2020 - 04:44 PM

Answered by admin AT 01/06/2020 - 04:44 PM

To calculate the number of years that the population of the town had been growing we proceed as follows;
A=p(1+r/100)^n
where;
A=final population
p=initial population
n=time
r=rate;
thus, substituting the values in the above formula we get:
28000=20000(1+15/100)^n
1.4=(1+0.15)^n
1.4=1.15^n
introducing natural logs we get:
ln1.4=nln1.15
n=(ln1.4)/(ln1.15)
n=2.4
thus;
n=2.4 years
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