To determine the number of years it will take for the standard of living to double given an annual labor productivity growth rate of 3 percent per year, we can use the "Rule of 70." This rule is a quick way to estimate the doubling time of an investment or, in this case, an economic growth rate.
Here's how the Rule of 70 works:
1. Identify the annual growth rate: In this scenario, the annual growth rate of labor productivity is 3 percent per year.
2. Apply the Rule of 70: The Rule of 70 states that you can estimate the doubling time by dividing 70 by the percentage growth rate.
[tex]\[
\text{Doubling Time} = \frac{70}{\text{growth rate percentage}}
\][/tex]
3. Insert the growth rate:
[tex]\[
\text{Doubling Time} = \frac{70}{3}
\][/tex]
4. Perform the division:
[tex]\[
\text{Doubling Time} \approx 23.33
\][/tex]
Rounding to the nearest whole number, the estimated number of years for the standard of living to double is about 23 years.
Therefore, from the given choices, the correct answer is:
- 23 years.
