Doubling Time?

Question

The time td$required for the solution y of the growth problem

y'=ky, k>0, y(0)=yo

to reach twice its original value is called the doubling time.

(a) Find the doubling time td in terms of k.

(b) Suppose that the solution of the above IVP has value B at any time t1 Determine the value of the solution at time t1 + td.

Answer 1

y=y(0)exp(ky)
so 2y(0)=y(0)=exp(ky)
so 2=exp(ky)
or ln(2)=ky
so ydouble=ln(2)/k