We're on the section of logarithms, so I'm guessing this has something to do with them...(adsbygoogle = window.adsbygoogle || []).push({});

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 = P_{0}a^{t}or P = P_{0}e^{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 = P_{0}a^{t}

2 = 1a^{5}

2 = a^{5}

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 = P_{0}e^{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?

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# Homework Help: Size of a bacteria colony

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