Exponential growth and decay - Higher

Money invested in a bank can generate two different types of interest. Compound interest occurs when interest is added to the balance at the end of a time period and interest is then calculated on the total of these at the end of the next time period.

If £10,000 is invested into an account offering 2% compound interest each year then the balance grows as shown in the table.

Year012345678910
Balance1,000.001,020.001,040.401,061.211,082.431,104.081,126.161,148.691,171.661,195.091,218.99
Balance of compound interest graph

This is an example of an exponential graph in the form y = k^x.

Graphs in the form of y = k^x increase in value.

Exponential graph showing y = k to the power of x

Solving problems with exponential growth

The graph shows how bacteria (y) grows over time (t). The equation of the graph is:

y = 20g^t

Exponential graph of y=20g^t

From the graph, when t = 2 y = 2,000.

Substituting these values into y = 20g^t:

2,000 = 20g^2

Dividing by 20 gives:

100 = g^2

Square rooting gives:

10 = g

So y = 20 \times 10^t.

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