Ratio, proportion and rates of changeKS3 / GCSE

Population growth using repeated percentages

Use percentage multipliers for repeated or successive changes.

  • The original amount is 100%. A increase leaves of the original amount.
  • is the multiplier: . Divide the percentage by 100 to write it as a decimal.
  • Use : is the initial amount, the multiplier for one year, the number of years and the final amount.
  • Keep the full value until the end. means more digits follow; round the final answer to the requested accuracy.

Example 1

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

The original amount is 100%. Add 1.5%; 101.5% remains. is the multiplier: 101.5% is 1.015 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 1.5%; 101.5% remains. is the multiplier: 101.5% is 1.015 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.

Example 2

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

The original amount is 100%. Add 2%; 102% remains. is the multiplier: 102% is 1.02 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 2%; 102% remains. is the multiplier: 102% is 1.02 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.

Your turn

Question 1

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

Check answer
The original amount is 100%. Add 2.5%; 102.5% remains. is the multiplier: 102.5% is 1.025 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 2.5%; 102.5% remains. is the multiplier: 102.5% is 1.025 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
Question 2

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

Check answer
The original amount is 100%. Add 3%; 103% remains. is the multiplier: 103% is 1.03 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 3%; 103% remains. is the multiplier: 103% is 1.03 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
Question 3

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

Check answer
The original amount is 100%. Add 3.5%; 103.5% remains. is the multiplier: 103.5% is 1.035 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 3.5%; 103.5% remains. is the multiplier: 103.5% is 1.035 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
Question 4

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

Check answer
The original amount is 100%. Add 4%; 104% remains. is the multiplier: 104% is 1.04 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 4%; 104% remains. is the multiplier: 104% is 1.04 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
Question 5

A town has people. A model predicts growth of per year. Estimate the population after years, to the nearest whole person.

Check answer
The original amount is 100%. Add 4.5%; 104.5% remains. is the multiplier: 104.5% is 1.045 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
The original amount is 100%. Add 4.5%; 104.5% remains. is the multiplier: 104.5% is 1.045 times the original amount.Apply the multiplier once for each year.Keep the full value until the final step.To the nearest whole person.
← All Ratio, proportion and rates of change cardsReport a mistake