# Math Help - E.Coli exponential growth problem, what am i doing wrong?

1. ## E.Coli exponential growth problem, what am i doing wrong?

E.Coli exponential growth problem, what am i doing wrong?
Okay, so I have found the correct formula for this problem, but for some reason I must be doing something wrong, because I can't get the right answer. Here is the Original Problem, and I will go through what I did:

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells.
a) find relative growth rate. k= 2.08 (thats right)
b) Find an expression for the number of cells after t hours. = P(t)=55e^(2.08t) (this is right)

now, for c) it asks: Find the number of cells after 5 hours
________ billion cells. however, the number I am getting by just plugging it into the calculator, is 1807279.412. So i divided it by 1000, and said that it is 1807.279 billion. But Is this wrong?

Also, how do I find the rate of growth after 5 hours?

I feel like I must be doing something kind of stupid, because it seems smile enough. Thanks!

2. Originally Posted by keeg
E.Coli exponential growth problem, what am i doing wrong?
Okay, so I have found the correct formula for this problem, but for some reason I must be doing something wrong, because I can't get the right answer. Here is the Original Problem, and I will go through what I did:

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells.
a) find relative growth rate. k= 2.08 (thats right)
b) Find an expression for the number of cells after t hours. = P(t)=55e^(2.08t) (this is right)

now, for c) it asks: Find the number of cells after 5 hours
________ billion cells. however, the number I am getting by just plugging it into the calculator, is 1807279.412. So i divided it by 1000, and said that it is 1807.279 billion. But Is this wrong?

Also, how do I find the rate of growth after 5 hours?

I feel like I must be doing something kind of stupid, because it seems smile enough. Thanks!
... are you sure the initial population was just 55 cells?

3. Yeah, its only 55 cells. here is the question verbatim:
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells. (The tolerance is 1% unless your instructor states otherwise.)

4. Originally Posted by keeg
Yeah, its only 55 cells. here is the question verbatim:
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 55 cells. (The tolerance is 1% unless your instructor states otherwise.)
$k = \ln(8)$

$P(t) = 55e^{kt}$

$P(5) = 55e^{5k} = 1802240$ cells

number of cells in billions ... (note that a billion is $10^9$)

$P(5) = \frac{1802240}{10^9} = 1.8 \times 10^{-3}$ billion cells

rate of growth is $\frac{dP}{dt} = kP$ ...

at $t = 5$ hrs, $\frac{dP}{dt} = 3.7 \times 10^6$ bacteria/hr