Page 11 - Mathematics Literacy Grade 11

Unit 4: Constant ratio relationship

A constant ratio relationship is where there is a constant ratio between the terms in
the pattern. When you invest or borrow money you will be charged interest on the
amount which you will then need to pay. If money is borrowed or invested and the
interest is calculated at a specific rate, e.g. 2%, the relationship that exists between
the amount of money owed or earned is classified as a constant ratio.

Example 3

A biologist was investigating the number of bacteria found on a piece of
bread over a 6 day period. She created a table and recorded her results.

Day 1 2 3 4 5 6
Number 50 150 450 1350 4050 12150
of
Bacteria

Every day the number of bacteria triples. We can therefore say that to get the next
day’s number you multiply the previous number by 3. Therefore the constant ratio is
3. We can create a rule for this relationship:

Amount of bacteria on the current day = the number of bacteria on the previous day x
3.

In this example the number of days is the independent variable and the number of
bacteria is the dependent variable.

Example 4

The table below shows the amount of money in a fixed deposit account over time.

Month 0 1 2 3 4
Account R2000 R2010 R2020.05 R2030.15 R2040.30
balance

The amount in the account is increasing by a constant ratio of 0, 5%. We can
therefore calculate the amount by using the following method:

Current month’s balance = previous month’s balance + 0, 5% of previous month’s
balance.

We can work out the constant ratio by dividing each term by the previous term.

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