The Mitscherlich model for agricultural production specifies that the size Q(t) of a crop changes at a rate proportional to the difference between the maximum possible crop size B and Q; that is,

a. Solve this separable equation for Q(t). Express your answer in terms of k and the initial crop size Q₀ = Q(0).

b. A particular crop has a maximum size of 200 bushels per acre. At the start of the growing season (t = 0), the crop size is 50 bushels and 1 month later, it is 60 bushels. How large is the crop 3 months later (t = 3)?

Transcribed Image Text:

dQ dt = k(B - Q)