Modeling survival with a differential equation

[PhysicsInNJ]

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^-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.

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.

 

[MexChemE]

Okay, here's a hint. If f(t) represents the fraction of people still enrolled after their initial visit, what does 1 - f(t) represent?

 

[Ray Vickson]

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^-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.

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.

Are you saying you do not know what 50% of 300 works out to? That is what you would have if $f(t) = 0.5$ applied to the initial 300.