How do I solve this problem?
2 answers:
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I think there is a mistake in the question. If f(x) = (3 / 2)^x
, then
x f(x)
0 1
40 11057332.32
If the scale is 10 units to one inch, then you will need a paper size of 1105733.232 inches!
As a reference, a graph is included in attachments.
To get a linear function 2 points are needed. Assuming the equation g(x) = m*x and taking the points of the aforementioned table, we can compute the slope as
m = (f(x2) - f(x1))/(x2 - x1)
m = (11057332.32 - 1)/(40 - 0)
m = 276434.283
Function g(x) = 276434.283*x pass at points (0, 1) and (40, 11057332.32). h(x) = 276434.283*x + 2 fulfill the requirement that h(x) is greater than f(x), for all x such that 0 ≤ x ≤ 40, but f(41) > h(41), because at the next point, the exponential function will growths faster than linear function (see figure).
