# Calculus Word Problem

• Oct 25th 2009, 05:44 PM
kashifzaidi
Calculus Word Problem
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 65 cells. (The tolerance is 1% unless your instructor states otherwise.)

(a) Find the relative growth rate.
(b) Find an expression for the number of cells after t hours.
(c) Find the number of cells after 6 hours.
(d) Find the rate of growth after 6 hours.
(e) When will the population reach 20,000 cells?

(a) k= http://img40.imageshack.us/img40/2720/paletteimage.gif

(b) P(t)=http://img40.imageshack.us/img40/6301/paletteimageu.gif

(c) 17039360 billion cells

(d)35432353 billion cells per hour

(e) 2.75 hour

According to the book only a and e are correct.

Any help(Wondering)
• Oct 25th 2009, 07:35 PM
tonio
Quote:

Originally Posted by kashifzaidi
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 65 cells. (The tolerance is 1% unless your instructor states otherwise.)

(a) Find the relative growth rate.
(b) Find an expression for the number of cells after t hours.
(c) Find the number of cells after 6 hours.
(d) Find the rate of growth after 6 hours.
(e) When will the population reach 20,000 cells?

(a) k= http://img40.imageshack.us/img40/2720/paletteimage.gif

(b) P(t)=http://img40.imageshack.us/img40/6301/paletteimageu.gif

(c) 17039360 billion cells

(d)35432353 billion cells per hour

(e) 2.75 hour

According to the book only a and e are correct.

Any help(Wondering)

Erasing those weird "billion" you wrote there, I find all the answers correct. Perhaps in part (b) it is writen $p(t)=65\cdot 8^t$ , but this is exactly the same as what you wrote.

Tonio