## Plotting Straight Line Graphs From Exponential Relationships

Given a straight line plotted on a graph we can estimate the values of the gradient and either using a point on the line or by estimating the y â€“ intercept, we can find the equation of the line in the formThe most convenient form in which to analyse the relationship between two variables x and y is the linear form, and we must see if, given a suspected relationship between two variables, we can construct a linear graph from the suspected relationship.

Suppose we suspect an exponential relationship between two variables. We also have the following data.

Time, t in s | 10 | 20 | 30 | 40 | 50 |

Mass m in g | 40.3 | 27 | 18 | 12.2 | 8.1 |

Our relationship will take the formTo transform this into a straight line we take logs of both sides obtaining,We recalculate the table.

Time, t in s | 10 | 20 | 30 | 40 | 50 |

log (m) | 3.696 | 3.296 | 2.890 | 2.501 | 2.092 |

And sketch the graph:

Comparingwithwe seeso andsothen