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The functions f(x) and g(x) are shown below:
f(x) = 0.05x
g(x) = (0.05)^x
Which statement best describes the graph of f(x) and g(x)?
The graph of g(x) will eventually exceed the graph of f(x).
The graph of f(x) will eventually exceed the graph of g(x).
The graphs will both have their y-intercept equal to 1.
The graphs will both have their y-intercept equal to 0.05
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f(x) is a positive linear function and therefore its y-values will continue to increase incrementally by 0.05 at each x-value.
On the other hand, g(x) is a negative exponential function and therefore it's y-values will continue to be reduced by 1/20 (= 0.05) at each x-value. Note: it's negative because its a-value is less than one -- that is, 0.05. This gives g(x) an overall negative slope.
So, f(x) will eventually out value g(x) at some point.