Question

Given the functions f(x) and g(x) below, find

all solutions to the equation f(x) = g(x)
graphically to the nearest hundredth.

Answer 1

x = -4.50

Explanation:

You want the solution to f(x)=g(x) for the functions f(x) = 0.4^x -4 and g(x) = 58.

Graph

The attachment shows a graph of the two functions. The solution to f(x) = g(x) is the x=coordinate of the point of intersection between the two curves:

x ≈ -4.50.

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Additional comment

Analytically, the solution is ...

0.4^x = 62 . . . . . . . add 4 to the equation f(x) = g(x)

x = log(62)/log(0.4) . . . . . take logarithms; divide by the coefficient of x

x ≈ -4.50417563059

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