How can I use logarithms to determine the growth rate of a bacteria colony?

[Jacobpm64]

We're on the section of logarithms, so I'm guessing this has something to do with them...

If the size of a bacteria colony doubles in 5 hours, how long will it take for the number of bacteria to triple?

I know that doubling time and all that stuff is independent of the amount of something you have...

Should I use P = P₀a^t or P = P₀e^kt ?

I'll just try it both ways to show some work, but I don't know which equation i'd be using...

first with P = P₀a^t
2 = 1a⁵
2 = a⁵
a = 2^1/5
a = 1.1487

3 = (1.1487)^t
ln3 = tln(1.1487)
t = ln3 / ln1.1487
t = 7.92473 hours


Now, to try using P = P₀e^kt

2 = 1e^5k
2 = e^5k
ln2 = 5k
k = ln2 / 5
k = .138629

3 = 1e^.138629t
3 = e^.138629t
ln3 = .138629t
t = ln3 / .138629
t = 7.92484 hours

very close answers, which one equation should i have used, and is the answer right?

 

[TeethWhitener]

A quick glance should convince you that $a=e^k$, so the answers are equivalent.