# Exponential growth and decay - Higher

Money invested in a bank can generate two different types of 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

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.

### Solving problems with exponential growth

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

$y = 20g^t$

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 $$y = 20 \times 10^t$$.

Move on to Test