Question

. The population of a town decreases by 3% every year. What would be the town's population in 17 years if it has a population of 75,000 now.

Answer 1

the town's population after 17 years is 44,685

Step-by-step explanation:

decrease = rate = 3% = 0.03

t = 17 years

Present population = a = 75,000

y = population after t years

Exponential growth formula:

`y=a(1+r)^t`

Since the poulation is decreasing, the formula becomes (exponential decay):

`y=a(1-r)^t`

inserting into the formula:

`\begin{gathered} y=75000(1-0.03)^(17) \\ y=75000(0.97)^(17) \end{gathered}`
`\begin{gathered} y\text{ = 75000(0.5958)} \\ y\text{ = 44,685} \end{gathered}`

Hence, the town's population after 17 years is 44,685