Question

Population Growth The population of a town of 5000

grows at the rate of 3% per year. (a) Determine an equation that

gives the population t years from now. (b) Find the population three

years from now. Give your answer to (b) to the nearest integer.

Answer 1

a)
`A=5000{(1.03)}^(t)`

b) 5464 inhabitants.

Explanation:

The formula used for compound interest becomes very helpful in this case.

`A=P{(1+r)}^(t)\\\\When:\\A = Final Value\\P = Initial Value\\r = Rate of Change (Decimal)\\t = Time (Years)`

Knowing this, we can easily calculate the value for any year, counting from the original 5000.

From this formula, we can derive a specific one that will serve for any value of t.

a)

`A=5000{(1+0.03)}^(t)\\A=5000{(1.03)}^(t)`

b) Apply the formula:

`A=5000{(1.03)}^(3)\\A=5000(1.092727)\\A=5463.635=5464`

The town will have 5464 inhabitants.