Question

Suppose an E. coli culture is growing exponentially at 37 ◦C. After 20 minutes at that temperature, there are 1.28×10^7 E. coli cells. After 60 minutes, there are 2.4×10^7 cells. How long does it take for the culture to have double the amount of cells that it had started with?

I do not know where to begin. I tried using the equation P(x)=Po e^kt but I don't know what to do because there would be two values for t.

Answer 1

You can do it that way, but I think simpler math will do..

amountfinal=amoutintial*(e)^.692 time/doubletime

amountfinal/amountintial=e^.692(t/doublettime)

so you are given two points...
2.4E7/1.28E7 = e^.692*40/timedouble

I am assuming the "after 60minutes"means 40 min after the first reading.

take the ln of each side

ln( 2.4/1.28)=.692*40/timedouble
solve for time to double.

Answer 2

Can I ask why you are using 0.692 in the exponent?