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Suppose an E coli culture is growing exponentially at 37 degrees celsius. After 20 minutes at that temperature, there are 1.28x10^7 E. coli cells. After 60 minutes, there are 2.4 x 10^7 cells. How long does it take for the culture to have double the amount of cells that it started with?

I'm a bit confused as to what values I use for y(t) and t. Initial would = 1.28x10^7 would y = 2.56x10^7 and t=40??

Thank you

Amanda
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1 Answers1

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Suppose the initial number of cells is $I$ and the growth factor per minute is $k$.

To find the time $t$ it takes for the initial number of cells to double, we need not know the initial number; instead, we need to find the growth factor $k$ and then find $t$ from the equation

$e^{kt}$ = $2$

From the data, we have

$I*e^{20k}$ = $1.28*10^7$

$I*e^{60k}$ = $2.4*10^7$

So,

$e^{40k}$ = $1.875$

$40k$ = $ln (1.875)$

$k$ = $0.015715$

Now to find the time $t$,

$e^{0.015715t}$ =$2$

from which we get

$t$ = approx. $44.1$ Minutes

Rao A.
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