True or false:

(1) By the rule of 72, it takes 36 years for a country’s income per person to be quadrupled if it grows by 4 percent every year.

The statement is **true**.

### Explanation:
The "Rule of 72" is a simple way to estimate the number of years required for an investment or quantity to double, based on a fixed annual growth rate. The formula is:

\[
\text{Doubling time (in years)} = \frac{72}{\text{growth rate (\%)}}
\]

In this case, the growth rate is 4%. Using the Rule of 72 to estimate the time it takes to double:

\[
\text{Doubling time} = \frac{72}{4} = 18 \, \text{years}
\]

Since the question asks about quadrupling (which is two doublings), it would take 18 years to double, and then another 18 years to double again. So:

\[
18 + 18 = 36 \, \text{years}
\]

Thus, it takes 36 years to quadruple income per person at a 4% annual growth rate.

Would you like more details or have any questions?

### Related Questions:
1. How does the Rule of 72 change for different growth rates?
2. Can the Rule of 72 be used for non-constant growth rates?
3. What is the mathematical derivation behind the Rule of 72?
4. How does compounding frequency affect the accuracy of the Rule of 72?
5. What are some real-world examples where the Rule of 72 is applicable?

**Tip:** The Rule of 72 provides an approximation, and the result becomes less accurate with very high growth rates or irregular growth patterns.

By the rule of 72, it takes 36 years for a country’s income per person to be quadrupled if it grows by 4 percent every year.

Discover how the Rule of 72 estimates the time required for income to quadruple at a 4% annual growth rate. This problem uses the formula 'Doubling time = 72 / growth rate' and explores the doubling concept applied twice to achieve quadrupling. Suitable for high school students in Grades 9-12.

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