8/17/2014 A logistic growth model of the form y = A/(B + C•e–Kx) can be used to describe the proportion of households, y, that owns a VCR at year, x, where A, B, C and K are constants. Express x as a function of y.
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8/17/2014 Solution. Cross-multiplying: By + Cy•e –Kx= A
=> By + Cy•e –Kx = A
=> Cy•e –Kx = A – By
=> e –Kx = (A – By)/Cy
Taking logarithms: -Kx = ln (A – By)/Cy
Or x = -1/K• ln [(A – By)/Cy]