AI generatedRatio, proportion and rates of changeKS3 / GCSE

Writing a growth or decay formula

Let P be the starting amount, the number of periods, and the multiplier for one period.

  • Let P be the starting amount, the number of periods, and the multiplier for one period.
  • For an increase of %, = () ÷ 100. For a decrease, = () ÷ 100.
  • Write A = Pm to the power . State what one period means and check that gives the starting amount.

Example 1

A quantity starts at 300 and increases by 2% each month. Write a formula for A after complete months.

The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

Example 2

A quantity starts at 320 and decreases by 3% each month. Write a formula for A after complete months.

The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

A quantity starts at 340 and increases by 4% each month. Write a formula for A after complete months.

Check answer
The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

When , the multiplier power is 1, so A = 340.

Question 2

A quantity starts at 360 and decreases by 5% each month. Write a formula for A after complete months.

Check answer
The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

When , the multiplier power is 1, so A = 360.

Question 3

A quantity starts at 380 and increases by 6% each month. Write a formula for A after complete months.

Check answer
The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

When , the multiplier power is 1, so A = 380.

Question 4

A quantity starts at 400 and decreases by 7% each month. Write a formula for A after complete months.

Check answer
The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

When , the multiplier power is 1, so A = 400.

Question 5

A quantity starts at 420 and increases by 8% each month. Write a formula for A after complete months.

Check answer
The starting amount is 100%.Convert the new percentage to a fraction of 100.This is the multiplier for one period.P is the initial amount; counts months.

When , the multiplier power is 1, so A = 420.

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