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Generating exponential values between 0 and 1 given a range of input values?

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Hi, How can I generate exponential values between 0 and 1 within a range of values? For example if I want a graph that increases exponentially between 3 and 22.5. so exp(3) = 0 and exp(22.5) = 1.0 How can I achieve this? Thanks

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step 1 - re-map 3-22.5 to 0-1
float remap( float input )
return (input-3) / (22.5-3)

step 2 - raise to an exponent
float output = pow( remap(input), 42 );

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