differential eq. bacteria growth

[rooney]

In a culture of bacteria, the number of bacteria increased sixfold in 10 hours. How ling did it take for the population to double?

I am trying to use the equation P=Ce^kt, but am unable to find values for C or k. I feel like I am missing something basic, but I can't think of what it is.

 

[Deleted member 4993]

In a culture of bacteria, the number of bacteria increased sixfold in 10 hours. How ling did it take for the population to double?

I am trying to use the equation P=Ce^kt, but am unable to find values for C or k. I feel like I am missing something basic, but I can't think of what it is.

\(\displaystyle P = P_0\cdot e^{kt}\)

\(\displaystyle \frac{P}{P_0} = e^{kt}\)

\(\displaystyle 6 = e^{k\cdot10}\)

from above find 'k'

Then find 't' when

\(\displaystyle \frac{P}{P_0} = 2\)

 

[rooney]

Ah, I see. I was trying to use x as the initial population, and 6x as the sixfold population. This got me nowhere when I plugged it into the equation. Thank you.