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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)

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