The count in a culture of bacteria was 800 after 2 hours and 51,200 after 6 hours.?

Question

(a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. Round your answer to the nearest whole number. The answer is 104%.
(b) What was the initial size of the culture? Round your answer to the nearest whole number. The answer is 100.
(c) Find a function that models the number of bacteria, ( n(t) ), after ( t ) hours. Round the rate ( r ) to two decimal places. The answer is ( 100e^{1.04t} ).
I am struggling with the following:
(d) Find the number of bacteria after 4.5 hours. Round your answer to the nearest hundred. The answer is not 200.
(e) When will the number of bacteria reach 100,000? Round your answer to two decimal places. The answer is not 66.42.
Thank you!

Anonymous · Accepted Answer

(a) I am unsure of the term.
(b) is correct.
(c) I would use n(t) = 100 * 2 ^ ( (t/2) * 3); your answer is similar and given the request for rounding no doubt what the teacher wants.
(d) You are so close you will kick yourself.  Just plug in and solve.
n = 100 e ^ (1.04 (4.5)) ~= 10,777 ~= 10,800 (I used Google for the math)
(e) Again, we plug in and solve.
100 000 = 100 e ^ (1.04 t)
10000 = e ^ (1.04 t)
Taking natural logs of both sides gets rid of the pesky e.
ln (10000) = 1.04 t
t= ln (10000) / 1.04 ~= 8.86 hours

Prof. Ellis Howell Sr.

The count in a culture of bacteria was 800 after 2 hours and 51,200 after 6 hours.?

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