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Interpret Real Life Exponential Graphs

In this worksheet, students will practise interpreting a real life situation that leads to an exponential graph.

'Interpret Real Life Exponential Graphs' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel,

Curriculum topic:   Algebra, Graphs of Equations and Functions

Curriculum subtopic:   Graphs Graphs of Equations and Functions

Difficulty level:  

Worksheet Overview

It quite often happens in a GCSE exam that you will be expected to deal with graphs that show real life situations.

In this activity, we will deal exclusively with exponential graphs.


What is an exponential graph?

An exponential graph is any graph that has the form f(x) =  ax

This will give the graph that looks like this:


an exponential graph


Exponential growth means that as one variable increases, the rate of increase of the other also increases - try saying that three times fast!



Bacteria are being grown in a dish and the results are recorded on a graph where the amount of bacteria is plotted against time:


an exponential graph


Describe the relationship between the time and the amount of bacteria.

This question will always have the same response. When the graph is like this, the bacteria are growing exponentially.


How long does it take to get to 3 million bacteria?

How many bacteria are in the dish after 6 hours?

Both of these can be done by using the graph line to convert between the two values:


an exponential graph

Reading from the graph, there are 3 million bacteria after approximately 4.9 hours and after 6 hours, there are approximately 5.3 million bacteria.


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