# Thread: Calculus Word Problem

1. ## 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?

My answers are :
(a) k=

(b) P(t)=

(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

2. 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?

My answers are :
(a) k=

(b) P(t)=

(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

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