Question

if the population of a city is 158,000 and isdecreasing by 8% every year, what will thepopulation be in 5 years?

Answer 1

From the question, we use the population decay formula expressed as

`\begin{gathered} P(t)=P(1-r)^t \\ where \\ P\Rightarrow initial\text{ population} \\ r\Rightarrow decay\text{ rate} \\ t\Rightarrow time \\ P(t)\Rightarrow population\text{ at time t} \end{gathered}`

Given that:

`\begin{gathered} P=158000 \\ r=8\%=(8)/(100)=0.08 \\ t=5 \end{gathered}`

By substituting these values into the population decay formula, we have

`\begin{gathered} P(t)=158000(1-0.08)^5 \\ =104134.88066 \end{gathered}`

Hence, the population in 5 years will be

`104134.88066`