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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.

User Synexis
by
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1 Answer

3 votes

Answer:

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.

User Wilmerton
by
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