Plot and Interpret Exponential Graphs
# Plot and Interpret Exponential Graphs

GCSE(H),

An exponential graph is generated from a function of the form `f(x)=m^x`.

The graph will be curved. They will typically show compound interest or compound growth. Because the graph is curved, use several points to plot the graph. In real-life situations, the graph normally shows positive values. In algebraic usage, the negative parts of a graph would also be shown.

## Examples

1. £250 is invested with a compound rate of 15%. The table below shows how the saving grows over 10 years. Plot the graph, and determine what the investment is worth after 5 years.

time | 0 | 2 | 4 | 6 | 8 | 10 |

value (£) | 250 | 330 | 437 | 578 | 765 | 1011 |

Answer: £503

After 5 years, £503 (any answer around £500 would be accepted). Draw up from 65 years to meet the graph, then along to read the value from the vertical scale.

2. From the graph, above, estimate to the nearest year how long would it take before the value of the investment is worth £800.

Answer: 8 years

Read along from £800 to meet the graph, then down for a value of 8.3 years, or 8 years to the nearest year.

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