On opposite sides of a major city two suburban towns are experiencing population changes. One town, Town A, is growing rapidly at 5% per year and has a current population of 39,000. Town B has a declining population at a rate of 2% per year. Its current population is 55,000. Economists predict that in 5 years the populations of these two towns will be about the same, but the residents of both towns are in disbelief. The economists also claim that ten years after that, Town A will double the size of Town B. Can you verify the predictions based on the data given? Do you think these predictions will come true?

Question

Clara

Mathematics

27 September, 19:42

On opposite sides of a major city two suburban towns are experiencing population changes. One town, Town A, is growing rapidly at 5% per year and has a current population of 39,000. Town B has a declining population at a rate of 2% per year. Its current population is 55,000. Economists predict that in 5 years the populations of these two towns will be about the same, but the residents of both towns are in disbelief. The economists also claim that ten years after that, Town A will double the size of Town B. Can you verify the predictions based on the data given? Do you think these predictions will come true?

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Answers (1)

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Kaylah Benson · Answer 1

Population of Town A in 5 years = 39,000 (1.05) ^5 = 49,775

Population of Town B in 5 years = 55,000 (0.98) ^5 = 49716

which are very close so the Economists are correct.

In ten years after that::-

Town A population will be 49,775 (1.05^10 = 81,078

Town B ... 49,716 * (0.98) ^10 = 40,621

Town A is almost double population of Town A. so that prediction is verified.

Whether they will come true or not depends on whether the 5 % growth and/or the 2 % decline will continue through the given time period.