Bacterial growth problem?
It is noon and we start with 1 bacteria which divides every minute. In 47 minutes, the petri dish is half covered in bacteria. Write an equation that expresses the growth rate. How long did it take for 1/3 of the petri dish to be covered in bacteria?
Update:Ok, I saw that I had to use P=AB^t, but I couldn't figure out what B was. How did you get 2 for B?
Comments
P = A * 2^t
t is in minutes
A = 1
P = 1 * 2^47
So, when P = 2^47, the dish is half full
The dish is 1/3 full when P = (2/3) * 2^47
(2/3) * 2^47 = 2^t
2^48 / 3 = 2^t
ln(2^48 / 3) = t * ln(2)
ln(2^48) - ln(3) = t * ln(2)
t = (48 * ln(2) - ln(3)) / ln(2)
t = 46.415037499278843818546261056052
46 minutes, 25 seconds