Answer:
"To the nearest year, it would be about 9 years"
Step-by-step explanation:
11c)
This is compound growth problem. It goes by the formula:
[tex]F=P(1+r)^t[/tex]
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:
[tex]F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t[/tex]
To solve exponentials, we can take Natural Log (Ln) of both sides:
[tex]2=(1.08)^t\\Ln(2)=Ln((1.08)^t)[/tex]
Using the rule shown below we can simplify and solve:
[tex]Ln(a^b)=bLn(a)[/tex]
We can write:
[tex]Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064[/tex]
To the nearest year, that would be about 9 years
