# Calc

posted by .

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 59 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 5 hours.

(d) Find the rate of growth after 5 hours.

• Calc -

Number = 59(2)^(t/20) where t is the number of minutes

so after 5 hours
Number = 59(2)^15
= 1933312

rate of growth
= d(Number)/dt
= (59ln2(2)^(t/20))/20
= (59/20)ln(2)^(t/20)

## Similar Questions

1. ### Physics

The bacterium Escherichia coli (or E. coli) is a single-celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, these bacteria swim along zig-zag paths at a …
2. ### calculus

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 51 cells. (a) Find the relative …
3. ### Calculus

The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a …
4. ### Chemistry

The Heisenberg Uncertainty Principle: A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of mm = 0.100fg\rm fg (where a femtogram, fg\rm fg, is 10−15g\rm 10^{-15}\; g) and is swimming …
5. ### Chemistry

The Heisenberg Uncertainty Principle: A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of mm = 0.100fg\rm fg (where a femtogram, fg\rm fg, is 10−15g\rm 10^{-15}\; g) and is swimming …
6. ### Urgent Chemistry

The Heisenberg Uncertainty Principle: A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of mm = 0.100fg\rm fg (where a femtogram, fg\rm fg, is 10−15g\rm 10^{-15}\; g) and is swimming …
7. ### Math

The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a …
8. ### Math

The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a …
9. ### Calculus

Suppose an E. coli culture is growing exponentially at 37 ◦C. After 20 minutes at that temperature, there are 1.28×10^7 E. coli cells. After 60 minutes, there are 2.4×10^7 cells. How long does it take for the culture to have …
10. ### Math

Mitosis is a process of cell reproduction in which one cell divides into two identical cells. A bacterium called E. coli often causes serious food poisoning. It can reproduce itself in 15 minutes. a) Starting with one bacterium, make …

More Similar Questions