- #1

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## Homework Statement

The only functions with a constant doubling time are the exponential functions P

_{0}e

^{kt}with k > 0. Show that the doubling time of linear function f(t) = a(t) + b at time t

_{0}is t

_{0}+ b/a.

## Homework Equations

n/a

## The Attempt at a Solution

With initial time t

_{0}, P = at

_{0}+ b

At some time t, P is doubled: at + b = 2P

t = (2P - b)/a

Plug in P and simplify:

t = (2at

_{0}+ b)/a

t = 2t

_{0}+ b/a

What am I doing wrong?