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## Homework Statement

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*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.

^{-t/20}.## Homework Equations

N/A

## 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.