Future Business Leaders of America (FBLA) Marketing Practice Test

If a small gift shop has grown its sales by 10% per year, how many years will it take to double its sales?

1. 5.0

2. 7.2

3. 10.5

4. 6.0

The correct answer is: 7.2

To determine how many years it takes for the sales of a gift shop growing at an annual rate of 10% to double, one can utilize the rule of 70 or the logarithmic approach to calculate growth. Using the rule of 70, which gives a quick estimation of the doubling time for an investment or growth scenario, you divide 70 by the annual growth rate. In this case, 70 divided by 10 gives approximately 7.0 years. This aligns closely with the choice that indicates it will take around 7.2 years, making this the most accurate estimate when comparing to the option provided. The logarithmic approach entails calculating the time (t) using the formula for continuous growth: \[ 2 = (1 + r)^t \] Here, r is the growth rate expressed as a decimal (0.10 for 10%). Solving this would lead to: \[ t = \frac{\ln(2)}{\ln(1 + 0.10)} \approx 7.27 \text{ years} \] This solution approximates closely to 7.2 years, confirming that the determination made aligns with sound mathematical principles related to growth rates and compound interest. Therefore, the answer that