Answer:
B) 25.82%
Explanation:
This equation will be in the form
[tex]y=a(1+r)^x[/tex],
where a is the initial value, x is the number of time periods and r is the annual rate of growth.
We know the initial value, a, is 0.12.
We know that x, the amount of time, is 2014-1969 = 45.
We know that y, the total value, is 3700.
This gives us the equation
[tex]3700=0.12(1+r)^{45}[/tex]
Divide both sides by 0.12:
[tex]\frac{3700}{0.12}=\frac{0.12(1+r)^{45}}{0.12}\\\\30833.33=(1+r)^{45}[/tex]
To find this, we must next take the 45th root. This is the same as raising to the power of 1/45:
[tex]30833.33^{\frac{1}{45}}=((1+r)^{45})^{\frac{1}{45}}\\\\1.2582=1+r[/tex]
Subtract 1 from each side:
1.2582-1 = 1+r-1
0.2582 = r
To convert this to a percent, multiply by 100:
0.2582(100) = 25.82%
