The Number Of Bacteria In A Petri Dish Doubles Every 20 Minutes.If A Colony Is Seeded With 20 Bacteria, How Long Will It Take Until There Are 200,000 Bacteria In The Dish? Round Of To Nearest 5 Minutes. Show Working Out Please.

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Oddman Profile
Oddman answered
The count of bacteria is given by the equation
count = 20(2t/20)
where t is the time in minutes.

We want to find t when count = 200,000.
200,000 = 20(2t/20)
10,000 = 2t/20 (divide by 20)
Log[10,000] = t/20*Log[2] (take the log of both sides)
Log[10,000]/Log[2]*20 = t (multiply both sides by 20/Log[2])
4/.30103*20 = t (find the numerical values)
13.288*20 ≈ t (perform the division)
265.75 ≈ t (perform the multiplication, recognize that 265 is divisible by 5)

To the nearest 5 minutes, the time required is 265 minutes. That is 4 hours, 25 minutes.

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