To determine how long it will take for a country's income to double with an 8 percent growth rate, we can use the Rule of 72. The Rule of 72 is a simple formula used to estimate the number of years required to double the value of an investment or, in this case, the income, given a fixed annual rate of growth.
Here is the step-by-step solution:
1. Identify the growth rate: The problem states that the growth rate is 8 percent.
2. Apply the Rule of 72: According to the Rule of 72, the number of years required to double the income can be found by dividing 72 by the growth rate.
3. Perform the calculation: Divide 72 by the growth rate of 8 percent.
[tex]\[
\text{Number of years} = \frac{72}{\text{Growth Rate}}
\][/tex]
Substituting the growth rate of 8 percent into the formula:
[tex]\[
\text{Number of years} = \frac{72}{8} = 9
\][/tex]
4. Conclusion: Therefore, with an 8 percent growth rate, it will take approximately 9 years to double the country's income.
Thus, the correct answer is:
C. 9 years.
