Abroth containing 1 million bacterial cells is treated with an antimicrobial agent that kills 90% of the cells in 1 minute. what is the minimum amount of time it will take before all the cells in the broth are dead?

The answer is 7 minutes.

After 1 minute:
   1,000,000 - 90% * 1,000,000
= 1,000,000 - 0.9 * 1,000,000
= 1,000,000 - 900,000
= 100,000

After 2 minutes:
   100,000 - 90% * 100,000
= 100,000 - 0.9 * 100,000
= 100,000 - 90,000
= 10,000

After 3 minutes:
   10,000 - 90% * 10,000
= 10,000 - 0.9 * 10,000
= 10,000 - 9,000
= 1,000

After 4 minutes:
   1,000 - 90% * 1,000
= 1,000 - 0.9 * 1,000
= 1,000 - 900
= 100

After 5 minutes:
   100 - 90% * 100
= 100 - 0.9 * 100
= 100 - 90
= 10

After 6 minutes:
   10 - 90% * 10
= 10 - 0.9 * 10
= 10 - 9
= 1

After 7 minutes:
   1 - 90% * 1
= 1 - 0.9 * 1
= 1 - 0.9
= 0.1

Since 0.1 is not a whole bacterial cell, 7 minutes are enough to kill all bacterial cells.