Question

Please help with 11c!?

Answer 1

"To the nearest year, it would be about 9 years"

Explanation:

11c)

This is compound growth problem. It goes by the formula:

`F=P(1+r)^t`

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

`F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t`

To solve exponentials, we can take Natural Log (Ln) of both sides:

`2=(1.08)^t\\Ln(2)=Ln((1.08)^t)`

Using the rule shown below we can simplify and solve:

`Ln(a^b)=bLn(a)`

We can write:

`Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=(Ln(2))/(Ln(1.08))\\t=9.0064`

To the nearest year, that would be about 9 years