# math

posted by .

A certain antibioyic reducesthe number of bacteria in your body by 10% each dose
a) if four doses of the antibiotic are taken, what percent of the original bacterial population is left.
b) biologists have determined that when a person has a bacterial infection, if the bacterial level can be reduced to 5% of its population, the person can fight off the infection. How many doses must be administered to reduce the bacterial population to the desired level?

Its a geometric question.

• math -

a) (0.9)^4 = 0.656 = 65.6% of original remains
b) Solve (0.9)^N = 0.05 for N

N = log(0.05)/log(0.9]= 28.4

• math -

Its shud be done without using log

• math -

Without log, you only have to multiply 1.0 by 0.9 as many times as need to get a product of 0.05. I get 0.052 after multiplying 28 times and 0.047 after multiplying 29 times.
So the answer is between 28 to 29 doses.

## Similar Questions

1. ### Math(geometric sequences)

A certain antibiotic reduces the number of bacteria in your body by 10% each does. a)If four does of the antibiotic are taken, what percent of the original bacterial population is left?
2. ### math

a certain antibiotic redues the number of bacteria in your body by 10% each dse, if 4 doses of the antibiotic are taken, what percent of the original bacterial population is left
3. ### Pre Calculus

When doctors prescribe medicine at equally spaced time intervals, they are aware that the body metabolizes the drug gradually. After some period of time, only a certain percent of the original amount remains. After each dose, the amount …
4. ### PreCalc

2000(1 – 0.75) = 2000 (.25) = 500 survivors after the dose of antibiotic a is taken Then, 500(1.40)3 = 1374 bacteria after the 3 hours period at the instant before the second dose is taken. a.) For antibiotic A, determine the bacterial …
5. ### PreCalculus

2000(1 – 0.75) = 2000 (.25) = 500 survivors after the dose of prescription a is taken Then, 500(1.40)3 = 1374 bacteria after the 3 hours period at the instant before the second dose is taken. 1.) For antibiotic A, determine the bacterial …

The concentration (in milligrams per liter) of an antibiotic in the blood is given by the geometric series: A + Aekt + Ae2kt + + Ae(n − 1)kt where A is the number of milligrams in one dose of the antibiotic, n is the number of …
7. ### math

The concentration (in milligrams per liter) of an antibiotic in the blood is given by the geometric series A + Aekt + Ae2kt + + Ae(n − 1)kt where A is the number of milligrams in one dose of the antibiotic, n is the number of …
8. ### Math

The concentration (in milligrams per liter) of an antibiotic in the blood is given by the geometric series A + Aekt + Ae2kt + + Ae(n − 1)kt where A is the number of milligrams in one dose of the antibiotic, n is the number of …
9. ### Ms. Sue PLZ HELP!!!(science)

Humans developed antibiotics to fight bacterial infections. However, some antibiotics are no longer effective in killing the bacteria they once killed. How does the theory of evolution explain this?
10. ### Science

1. Humans developed antibiotics to fight bacterial infections. However, some antibiotics are no longer effective in killing the bacteria they once killed. How does the theory of evolution explain this?

More Similar Questions