A common inhabitant of human intestines is the bacterium Escherichia coli. A cel

Question

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 57 cells.

(a) Find the relative growth rate. (Assume t is measured in hours.)

k = ln(8)

(b) Find an expression for the number of cells after t hours.

P(t) = 57(8)^t

(c) Find the number of cells after 8 hours.

956,301,312 cells.

(d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.)

________________billion cells per hour

(e) When will the population reach 20,000 cells? (Round your answer to two decimal places.)

________________hr

Explanation / Answer

a)relative growth rate =

ek -1 = N(t+1)-N(t)/N(t)

N(0)= 1

N(1) = 8 (after 1) hr

ek -1 = 8 -1/1

k= ln(8)

b)using above eq. we can write

p(t) = 57*8^t

c)after 8 hours

p(8) = 57*8^8 = 956301312

d)growth rate = p(8)*k

                    = 956301312*ln(8)= 1988572675

e)20,000 = 57*8^t

t = 2.81 hr

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.