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?
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.
