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.
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.
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 \(y = 20 \times 10^t\).