Question

A city’s population has decreased 30% over the past 15 years. What annual percent decrease does this correspond to (hint: it’s not 2%)?

A) 2%
B) 3%
C) 5%
D) 7%

Answer 1

The annual percent decrease corresponding to a 30% population decrease over 15 years is found by rearranging the compound interest decay formula and approximating the value of r using a calculator, which will be close to but not exactly 2% due to compound decay.The answer is: C) 5%

Step-by-step explanation:

The annual percent decrease is not 2% because the population decreased by 30% over 15 years, which is a significant decrease. To calculate the annual percent decrease, we can use the formula:

Annual Percent Decrease = (1 - Final Population / Initial Population) * 100

Let's say the initial population was 100,000 and the final population was 70,000.

Annual Percent Decrease = (1 - 70,000 / 100,000) * 100

Annual Percent Decrease = -4.67% (rounded to two decimal places)

So the annual percent decrease is not 2%, but closer to -5%. However, since we're rounding to two decimal places, we'll use -5% as our answer.

The answer is: C) 5%