Exponential Growth?

Gfrant7 · #1 $Old$ 09-07-2008, 02:41 PM

If the size of a bacteria colony doubles in 5 hours, how long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

I'm not really sure where to start here, but I'm assuming it has something to do with y=cb^t?

Jhevon · #2 $Old$ 09-07-2008, 02:45 PM

Quote:

Originally Posted by Gfrant7 $View Post$

If the size of a bacteria colony doubles in 5 hours, how long will it take for the number of bacteria to triple? Give your answer in exact form and decimal form.

I'm not really sure where to start here, but I'm assuming it has something to do with y=cb^t?

the formula for exponential growth is

$P(t) = P_0e^{rt}$

where $P(t)$ is the amount after time $t$ , $P_0$ is the initial amount and $r$ is the rate of growth.

another useful formula (which can be derived from the formula above) is:

$T = \frac {\ln 2}r$

where $T$ is the time to double the amount. you can use this to find $r$ .

Now, you are asked for the time it takes for the following to happen

$3 P_0 = P_0e^{rt}$

do you see that? can you continue?