An infectious strain of bacteria increases in number at a relative growth rate of 200% per hour. When a certain critical number of bacteria are present in the bloodstream, a person becomes ill. If a single bacterium infects a person, the critical level is reached in 24 hours. How long will it take the critical level to be reached if the same person is infected with 10 bacteria?

It will take 2.4 hours or 2 hours 24 minutes for the critical level to be reached if a person gets infected with 10 bacteria

Step-by-step explanation:

*From the question, bacteria increases in number at a growth rate of 200 percent per hour

*If one bacterium infects Mrs Williams for example, in 24 hours Mrs Williams will fall ill.

*Now this means that one bacterium growing at 200% per hour in Mrs Williams' body must have grown to 4800% in 24 hours for her to fall ill

That is: 200%1hour

?% 24hours

24/1 ×200 =4800%

Now, if 10 bacteria infects Mrs Williams, how long will it take for her to fall ill? (In another way, when will the critical level of 4800% bacteria be reached?)

1 bacterium grows at 200% in 1 hour

10 bacteria will grow at ?% in 1 hour

That is, 10/1 × 200 = 2000%

This means that 10 bacteria will grow at 2000 percent per hour.

So, if 10 bacteria grows at 200% per hour and consequently infects Mrs Williams, they will grow to 4800% in 2.4 hours and thereby causing the woman to fall sick in just 2.4 hours

That is, 10 bacteria grows at 2000%1hour

They'll grow to 4800% in ? hours

= 4800/2000 ×1= 2.4 hours.

Since 60 minutes make 1 hour, 0.4 hours will be: 0.4 ×60 = 24 minutes

Therefore the time required for 10 bacteria infecting a person to reach a critical level before he/she becomes ill is 2hours 24 minutes