Mapping one range into another in an exponential but computationally cheap fashion

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I have a continuous variable x whose range is within [0, r], and a target range of [0, u]. I can linearly transform one range into the other by doing x/r * u, but I would like to do this in an exponential fashion (where bigger values of the first range map to bigger and bigger values of the second. I can have, arbitrarily, (x/r)^3 * u. However, is this the best solution? Especially considering that calculating (x/r)^3 is not computationally cheap.