The table below gives the percentage, $P$, of households with a VCR, as a function of year.

 Year 1978 1979 1980 1981 1982 1983 1984 P 0.3 0.5 1.1 1.8 3.1 5.5 10.6 Year 1985 1986 1987 1988 1989 1990 1991 P 20.8 36 48.7 58 64.6 71.9 71.9
(a) A logistic model is a good one to use for these data. Explain why this might be the case: logically, how large would the growth in VCR ownership be when they are first introduced? How large can the ownership ever be?
We can also investigate this by estimating the growth rate of $P$ for the given data. Do this at the beginning, middle, and near the end of the data:
$P'(1980) \approx$
$P'(1985) \approx$
$P'(1990) \approx$
Be sure you can explain why this suggests that a logistic model is appropriate. (b) Use the data to estimate the year when the point of inflection of $P$ occurs.
The inflection point occurs approximately at .
(Give the year in which it occurs.)

What percent of households had VCRs then? $P =$

What limiting value $L$ does this point of inflection predict (note that if the logistic model is reasonable, this prediction should agree with the data for 1990 and 1991)?
$L =$

(c) The best logistic equation (solution to the logistic differential equation) for these data turns out to be the following. What limiting value does this predict?
$L =$