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(2

10,000 = 2

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.

count = 20(2t/20)

where t is the time in minutes.

We want to find t when count = 200,000.

200,000 = 20(2

^{t/20})10,000 = 2

^{t/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.