Question

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.

Answer 1

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

Answer 2

Its shud be done without using log

Answer 3

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.