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
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