The population in a small town is increasing annually by 2.8%. What is the quarterly growth rate of the population? (hint: express your answer in percent ).

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asked Dec 26, 2024 192k views

1 Answer

Vinayak Shahdeo · Answer 1 · 2024-12-31T21:08:47+0000

The quarterly growth rate of the population is 0.7%.

To find the quarterly growth rate, we need to convert the annual growth rate to a quarterly growth rate.

Step 1: Convert the annual growth rate to a decimal by dividing it by 100.

p = 2.8/100 = 0.028

Step 2: Find the quarterly growth rate by taking the fourth root of the decimal.

q = (1 + p)^(1/4) - 1

q = (1 + 0.028)^(1/4) - 1

q = 0.007

Step 3: Multiply the quarterly growth rate by 100 to express it in percent.

Quarterly growth rate = 0.007 * 100 = 0.7%