Derive the formula for the tripling time for P = Po * a^(nt). What does this tripling time NOT depend on?

Question

Do we need to make any assumptions about a and n?

Answer 1

For the thing to grow: a>1 and n>0
Evaluate the expression at P = 3P, and time being an unknown "s"

so 3P=Po * a^(n s)

now take the ratio of the 2 results:

3 = a^(n s)/a^(n t) = a^(n*(s-t))

solve for s, by taking log of both sides:

log(3)=n*(s-t)*log(a)

so tripling time, s:

s = t + 1/n log(3)/log(a)

Answer 2

As answer 1 states, a must be >1 and N >0. I don't agree with the "t +" in answer 1's final equation. We want to solve for time t such that P = 3Po = Po * a^(n*t). Then a^(n*t) = 3, and n*t = LOG-base-a(3) = log(3)/log(a). Rearranging,
t = log(3)/(n*log(a))
The tripling time does not depend on Po.

Answer 3

que