5.3 Growth and Decay Factors

Suppose you want to increase or decrease a quantity by a percentage. At school, you may well have done it as in the next example.

Example 5.3a
Jimmy used to get £4.50 a week pocket money. After his birthday he was promised a 10% rise, if he could work the new amount out correctly. What should his new weekly allowance be?

Solution:
Jimmy’s increase is 10% of £4.50 which is £0.45.

Another way of calculating this is as follows.

If you think of his old amount (£4.50) as 100%, an increase of 10% will now give Jimmy 110%.
Now, any percentage means ‘over 100’, so 110% = 110/100 = 1.10.
Multiplying the old amount £4.50 by 1.10 automatically gives you £4.95, the new, increased quantity.

We call the number 1.10 a growth factor.