Thread: Logarithmic Modeling problem

Ok I've been quite stuck on this for a little while and as always, I have the worst time setting up the problem.


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 for the the critical level to be reached if the same person is infected with 10 bacteria?


I know we use the exponential growth formula but i'm uncertain as to how to set it up with the problem.

Originally Posted by JonathanEyoon

Ok I've been quite stuck on this for a little while and as always, I have the worst time setting up the problem.


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 for the the critical level to be reached if the same person is infected with 10 bacteria?


I know we use the exponential growth formula but i'm uncertain as to how to set it up with the problem.

The number doubles in 1 hour, so N=2^t, where t is measured in hours from
infection.

To grow to 10 it would take:

t = log_2(10) hours

Therefore they will fall ill 24-log_2(10) = 24-3.32 = 20.68 hours after infection with 10 bacteria.

RonL