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Plotting Line 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 – 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 ins

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 ins

10

20

30

40

50

log (m)

3.696

3.296

2.890

2.501

2.092

And sketch the graph:

Comparingwithwe seeso andsothen