The only functions with a constant doubling time are the exponential functions P0ekt with k > 0. Show that the doubling time of linear function f(t) = a(t) + b at time t0 is t0 + b/a.
The Attempt at a Solution
With initial time t0, P = at0 + b
At some time t, P is doubled: at + b = 2P
t = (2P - b)/a
Plug in P and simplify:
t = (2at0 + b)/a
t = 2t0 + b/a
What am I doing wrong?