Wendy is looking over some data regarding the strength of some rope and how that relates to its number of woven strands. The data seem to be exponential. How can Wendy determine if the data are exponential, and how can she convert that to a logarithmic function?

Question

Virginia Fuentes

Mathematics

1 February, 12:10

Wendy is looking over some data regarding the strength of some rope and how that relates to its number of woven strands. The data seem to be exponential. How can Wendy determine if the data are exponential, and how can she convert that to a logarithmic function?

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Barajas · Answer 1

The best way is to draw the variables in a logarithmic paper.

The same result is obtained if you convert the data to logarithm. This is how you do it.

Suppose the the relation is exponential, call y the independent variable, x the dependent variable. The the relation can be written as y = C (A^x}

Apply logarithm to both sides

log[y] = log [C (A^x) ]

Now apply properties of logarithm function to the right side

log[y] = log [C] + x log[A]

Then if you plot log[y] vs log [A] the graph is a straight line where log [C] is the y-intercept and log[A] is the slope.