Question

the population of askewville in 2016 was 229 and is declining at 3% per year. If this trend continues, when will the population of askewville reach 100 residents?

Answer 1

Around 27.2 years later

Explanation:

This is compound decline problem. We use the formula:

`F=P(1-r)^t`

Where

F is future amount (100)

P is present amount (229)

r is the rate of decrease (3% means 3/100 = 0.03)

t is the time in years (which we want to find)

So, lets substitute and solve:

`F=P(1-r)^t\\100=229(1-0.03)^t\\100=229(0.97)^t\\0.4367=0.97^t\\ln(0.4367)=ln(0.97^t)\\ln(0.4367)=t*(ln0.97)\\t=(ln(0.4367))/((ln0.97))\\t=27.2`

So, around 27.2 years later, the population would reach 100