If a population of a town increases by 15% in one year and then decreases by 10%

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What’s inside this PDF?

Question: If a population of a town increases by 15% in one year and then decreases by 10% the next year, what is the net percentage change in the population over the two years?

Options:

5%
3.5%
4.5%
6%

Correct Answer: 4.5%

Solution:

Let the initial population be 100. After a 15% increase, it becomes 115. After a 10% decrease, it becomes 115 - 11.5 = 103.5. The net change is (103.5 - 100) / 100 * 100% = 3.5%.

If a population of a town increases by 15% in one year and then decreases by 10%

Practice Questions

If a population of a town increases by 15% in one year and then decreases by 10% the next year, what is the net percentage change in the population over the two years?

5%
3.5%
4.5%
6%

Questions & Step-by-Step Solutions

If a population of a town increases by 15% in one year and then decreases by 10% the next year, what is the net percentage change in the population over the two years?

Step 1: Assume the initial population of the town is 100.
Step 2: Calculate the population after a 15% increase. This is done by multiplying 100 by 0.15 (which is 15%) and adding it to the initial population: 100 + (100 * 0.15) = 115.
Step 3: Calculate the population after a 10% decrease from the new population of 115. First, find 10% of 115 by multiplying 115 by 0.10, which equals 11.5. Then subtract this from 115: 115 - 11.5 = 103.5.
Step 4: Find the net change in population by subtracting the initial population from the final population: 103.5 - 100 = 3.5.
Step 5: Calculate the net percentage change by dividing the net change by the initial population and multiplying by 100: (3.5 / 100) * 100% = 3.5%.

Percentage Change – Understanding how to calculate percentage increases and decreases in a population.
Compound Changes – Recognizing that successive percentage changes are not simply additive.

If a population of a town increases by 15% in one year and then decreases by 10%

What’s inside this PDF?

If a population of a town increases by 15% in one year and then decreases by 10%

Practice Questions

Questions & Step-by-Step Solutions

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