Question

The yearly capita consumption of whole milk in the US reached a peak of 40 gallons in 1945. It has been steadily decreasing at a rate of about 2.8% per year. How do you find an exponential model M(t) for capita whole milk consumption?

Answer 1

Exponential model does not befit this problem .Since, 1945, the model for consumption is `M(t) = 40 - 1.12 t` gallons,.At this rate, the consumption would have become nil by 1981.

Explanation:

Exponential fit is for growth/decay problems, wherein the rate of

growth/decay is tending to `oo`/0, as `t to oo`,

So rate of growth/decay is increasing, with respect to time.

Here, the rate is said to b steady.

M'=-2.8%=-(0.126)(40)=-1.12 gallom /year.

integrating,

`M=-1.12 t` + initial value= `40-1.12 t`

M becomes 0, when t =40/1.12 = 35.7... years.