**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*.

**Scroll
down for the solution.**

**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)/C****y****]**