Answer:
a) [tex]A=5000{(1.03)}^{t}[/tex]
b) 5464 inhabitants.
Step-by-step explanation:
The formula used for compound interest becomes very helpful in this case.
[tex]A=P{(1+r)}^{t}\\\\When:\\A = Final Value\\P = Initial Value\\r = Rate of Change (Decimal)\\t = Time (Years)[/tex]
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)
[tex]A=5000{(1+0.03)}^{t}\\A=5000{(1.03)}^{t}[/tex]
b) Apply the formula:
[tex]A=5000{(1.03)}^{3}\\A=5000(1.092727)\\A=5463.635=5464[/tex]
The town will have 5464 inhabitants.
