Alan

Here's another example with completely different functions, but with the same values of f`(5), g(2) etc.:

Still get 96.  More than a coincidence!

(7^3)/(7^4)  →  7^(3-4)  →  7^(-1)  → 1/7

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1/2^-3  →  2^3 →  8

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Rate of change between (x1, y1) and (x2, y2) is  (y2 - y1)/(x2 - x1)

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See the answer given here: http://web2.0calc.com/questions/need-help_79616#r4 

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100^(3/2)  →  (100^(1/2))^3  →  10^3  →  1000

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g(x) = log₁₀(x)  

g(1/1000) = log₁₀(1/1000)   →   log₁₀(10^-3)   →   -3

(log₁₀(10^m) = m)

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Equate the proportions:

s/5 = 75/15

s = 5*75/15

s = 5*5 → 25 ml

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You need an iterative numerical method.  For example:

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\(((-3)^{-3})^{-4}\rightarrow(\frac{1}{(-3)^3})^{-4}\rightarrow(\frac{1}{-27})^{-4}\rightarrow(-27)^4\rightarrow 531441\)

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