Please do question 1 part a,b,c,d, and e. Thank you. A common inhabitant of huma

Question

Please do question 1 part a,b,c,d, and e. Thank you. A common inhabitant of human intestines is the bacterium Escherichia co . A cell of this bacterium in a broth medium divides into two cells every 20 minutes. The initial population of a culture is 57 cells. Find the relative growth rate. (Assume t is measured in hours.) k = Find an expression for the number of cells after 1 hours. P9t) = Find the number of cells after 8 hours. Cells Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr

Explanation / Answer

a)

N(t) = N(0)e^kt

t = time = 20 min = 1/3 hr

k = relative growth rate (a positive number)

N(0) = initial population = 57

N(t) = population after a time t has passed = 57*2

57*2= 57e^(k/3)

2 = e^(k/3) , solving we have

b) expression N(t) = 57 *e^(2.0794 * t) ------aNSWER b

c) N (8) = 57 * e^(2.0794 * 8 ) = 9.56 × 10^8 ----ANSWER C

d) rate of growth = dN/dt = No * k * e^(kt) = k* N(t)

= 2.0794 * 9.56 * 10^8 =1.988 Billion cells/hr -----ANSWER d

e) 20000 = 57 * e^(2.0794 * t) , solve for t , we get

t = 2.818 hours -----ANSWER e

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