Thread: Infectious Bacteria

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


this is very hard.....

but the correct answers is 22.85 hour

pls solve it thanks

What have you done, except lookup the correct answer?

dude,, i tried to solve it but im wrong

heres what ive done

7.01 x 10 ^20 = e^24

then i solve for 7.01 x 10 ^ 21 e^2t

and i got t which is also 24 hours..

i look in book, and it says 22.85 hours..

if u can help then go on, otherwise keep quiet

First you have to understand what "relative growth rate of 200%" actually means. If the number of bacteria at the beginning (time t=0) is n=1, what will their number be in one hour, 2 hours, 3 hours.

Post back what you get.

After that you might be able to deduce how to calculate the number N of bacteria after 24 hours. That N number of bacteria is making a person ill.

Then you have to see when will that N number of bacteria be reached if you start off not with just one bacteria, but 10.

Then again you have to see what will the number of bacteria be after one, two, three hours (with respect to same relative growth rate) and deduce how would you calculate the number of bacteria after k hours, meaning you'd have to come up with the expression in variable k.

Then you can form the equation setting that expression equal to mentioned number N and calculate the number of hours k needed to reach that number of bacteria.

Originally Posted by aeroflix

dude,, i tried to solve it but im wrong

heres what ive done

7.01 x 10 ^20 = e^24

then i solve for 7.01 x 10 ^ 21 e^2t

and i got t which is also 24 hours..

i look in book, and it says 22.85 hours..

if u can help then go on, otherwise keep quiet

You're supposed to let us know what you have done prior to posting. And your attitude is something you should work on, alongside with your math!