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?
Exponential model does not befit this problem .Since, 1945, the model for consumption is
Exponential fit is for growth/decay problems, wherein the rate of
growth/decay is tending to
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.
M becomes 0, when t =40/1.12 = 35.7... years.