# 4

This problem requires some thought and advance planning. In fact, the calculations are simple enough that manual calculations are the most efficient means of working this problem. The following approach is included simply to demonstrate the steps that would be used in a Maple solution to this problem.

The key is to obtain a formula for the straight line in the graph. (Be sure you see where this comes from!)

> lng := 0.7 + 0.3*x;

As a check, let's try to duplicate the plot in the handout :

> plot( lng, x=0..3, 0..1.6, title=`Graph of ln( g(x) )` );

>

At present we know that and need to solve this equation for . There are a number of ways to do this, but one is to notice that , so that

> g := exp( lng );

And, finally, to force Maple to simplify this result we need to use the expand command (check that simplify does not yield the same results)

> g:= expand( g );

> plot( g , x = 0 .. 3, title =`Graph of g(x)`);

>

This explains why "logarithmic plots" are used: all exponential plots look more or less the same, and it is certainly difficult to read

the coefficient 2.01375 and the growth rate 0.3 off the graph. But the equivalent values of 0.7 and 0.3 were easy to get off the straight line plot of ln(g(x)).