# 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?

Aug 5, 2016

Exponential model does not befit this problem .Since, 1945, the model for consumption is $M \left(t\right) = 40 - 1.12 t$ 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 $\infty$/0, as $t \to \infty$,

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.