# Logarithmic Modeling problem

• Sep 24th 2007, 04:20 PM
JonathanEyoon
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?

:confused: I know we use the exponential growth formula but i'm uncertain as to how to set it up with the problem.
• Sep 25th 2007, 03:49 AM
CaptainBlack
Quote:

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?

:confused: 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