Repeated Change (SQA National 5 Maths): Revision Note

You should be familiar with calculating percentage increases and decreases from your National 4 Maths course.

For example, to increase an amount by 5%

• The new amount will be 100%+5%=105% of the original amount

• As a decimal number, 105%=1.05

• So multiply the original amount by the multiplier, 1.05, to find the new amount

Or to decrease an amount by 5%

• The new amount will be 100%-5%=95% of the original amount

• As a decimal number, 95%=0.95

• So multiply the original amount by the multiplier, 0.95, to find the new amount

The population of voles in a nature reserve is 8000 at the start of 2025.

Due to a new road being built across the reserve, the population is expected to fall by 5% each year.

Calculate the total population of voles expected to be in the nature reserve at the start of 2028.

Answer:

The multiplier for a 5% decrease is 0.95

But this occurs three times in a row (three years from start of 2025 to start of 2028)

So multiply 8000 by 0.95³

6859 voles

A museum has a collection of stamps. At the start of 2023 there were 3750 stamps in the collection.

During 2023 the museum increased the size of the collection by 7%.

During 2024 the number of stamps held at the start of the year was increased by a further 4%.

How many stamps were in the museum's collection at the start of 2025?

Answer:

The percentage multipliers are

• 1.07 for an increase of 7%

• 1.04 for an increase of 4%

These increases occur one after the other, so multiply 3750 by 1.071.04

4173 stamps