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) = a ^{x}**

This will give the graph that looks like this:

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

**Example:**

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

**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:

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.**

Time for some questions.