Question

Suppose you're going to sell a product, and your marketing team has determined that the maximum number of units of the product that can be sold is given by a constant M>0 and that the rate of increase in unit sales will be proportional to the difference between M and the number of units that have currently been sold. Then the cumulative number of units M>0 sold for any time t will be given by a function of the form:
A. U(t) = Ae^(-kt) - M
A. U(t) = Ae^(kt)
A. U(t) = Ae^(-kt) + M
A. U(t) = Ae^(kt) - M
A. U(t) = Ae^(kt) + M
(A is some undetermined constant, and k>0 is some proportionality constant)

Answer 1

Oops the answer choices should be A - E

Answer 2

you know that
du/dt = k*(M-u)
du/(M-u) = k dt
du/(u-M) = -k dt
ln(u-M) = -kt + c
u-M = e^c * e^(-kt)
u = Ae^(-kt) + M