A health club is opened, the fraction of members still enrolled t months from their initial visit is given by the function f(t)= e-t/20. the club initially accepts 300 members and will accept new members at a rate of 10 per month. How many people will be enrolled 15 months from now.
The Attempt at a Solution
I remember my professor referencing this problem could be done as a differential equation problem instead of a survival/renewal problem (which I can do).
Following the idea of inflow-outflow, I came up with
dP/dt= 10 (inflow) - ?
with P being members
I'm not sure how to take the fraction of people and make that into a rate.
Once I figure that out I could likely solve the differential normally for P.