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Find a function (logarithmic/exponential) to model the following graph. Be sure to...

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foxwit | Student, Undergraduate | (Level 1) Salutatorian

Posted July 20, 2013 at 2:35 PM via web

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Find a function (logarithmic/exponential) to model the following graph.

Be sure to show all work in coming up function.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 20, 2013 at 2:46 PM (Answer #1)

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You need to identify a point located on the given graph, hence, you may notice that for `x = 2, y = 3` , hence, you can set up the following logarithmic function, such that:

`y = log_a x`

Replacing `2` for `x` and `3` for `y` yields:

`3 = log_a 2 => a^3 = 2 => a = root(3)2`

Since the base of logarithm is now known, you may predict the model of logarithmic function, such that:

`y = log_(root(3)2) x`

Hence, evaluating the logarithmic function whose equation models the given curve, yields `y = log_(root(3)2) x` .

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