Suppose that P is a function which satisfies P'(t)=rP(t) for some constant r and P(t+11)=4P(t)
Find r.
How do i start this?
I would start by integrating: dP/dt= rP(t) separates into dP/P= r dt.
Integrate both sides of that. Notice that P(t+11)= 4P(t) for all t. Take t= 0 to get an equation that will let you find r.