In order to answer exam questions related to repeated proportional change, you will first need to understand some related mathematical terms:
The mathematical term 'proportional' describes two quantities which always have the same relative size or 'ratio'. For example;
An object weighs 2kg on the 1st day. If weight is proportional to age, then the object will weigh 4kg on the 2nd day, 6kg on the 3rd day, 8kg on the 4th day, 10kg on the 5th day and so on.
The mathematical term 'ratio' defines the relationship between two numbers of the same kind. The relationship between these numbers is expressed in the form "a to b" or more commonly in the form:
a : b
A ratio is used to represent how much of one object or value there is in relation to another object or value. For example:
If there are 10 apples and 5 oranges in a bowl, then the ratio of apples to oranges would be 10 to 5 or 10:5.
This is equivalent to 2:1.
In contrast, the ratio of oranges to apples would be 1:2.
The mathematical term 'iteration' means to repeat an operation. Similarly to the worked examples outlined in the 'Functions' revision guide, iterations involve inputting a value into a function, receiving an output value, and then using this output value as the input value for the function. For example:
To iterate the function 2x + 3, first you place any value of x into the function:
So if x = 1, then 2x + 3 = 5
Now you must take this output value of 5 and put it into the original function.
Therefore, when x = 5 , then 2x + 3 = 13
By continuing these iterations, you will be presented with an infinite sequence of numbers:
5, 13, 29, 61, .......