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The growth of a bacterial colony is calculated with the equation B=400*2.1^t with B being the amount of bacteria and t the time in hours. 

a. Calculate after how many minutes the amount of bacteria has grown to 12000. Give your answer in hours and minutes.

b. Calculate the growth factor per 20 minute time period. 

c. By how much percent does the amount of bacteria increase every minute?

 Mar 31, 2020
 #1
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B=400 x 2.1^t
a. 12000 =400 x 2.1^t, solve for t
[12000/400]  = 2.1^t
t=4.58 hours - or ~4 hours and ~35 minutes

 

b. [4 hours x 60 minutes + 35 minutes]=275 minutes.
[275 / 20] =13.75 - 20-minute periods
[12000 / 400]^(1 / 13.75) = 1.2806 - 1 x 100 =28.06% - Growth rate per 20-minute periods.

 

c. [12000 / 400]^(1/275) =1.01244 - 1 x 100 =1.244% - Growth rate per minute.

 Mar 31, 2020
 #2
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Hi! thanks for the answer. I'm just confused as to how you got 4.58 hours. I can't get an answer that is even near that

Guest Mar 31, 2020
 #3
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Take the log of: 12000 / 400 =30

 

Log(30) / log(2.1) =4.58 hours.

Guest Mar 31, 2020

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