Question

Population Growth The population of a town of 5000

Answer 1

Answer:

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

b) 5464 inhabitants.

Step-by-step 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.