Your baby brother has an ear infection. The doctor said there are probably 50,000,000 bacteria in his left ear. The penicillin that the doctor prescribed will k**l 7% of the bacteria every 6 hours. He is contagious until there are fewer than 100,000 bacteria. How long until he is no longer contagious?
100,000 =50,000,000 * 0.93^n
Divide both sides by 50,000,000
Take the log of both sides
n =log(0.002) / log(0.93)
n=85.6 hours = ~86 hours - when the baby is no longer contagious, or just over 3 ½ days.
so it is the equation 50000000*(0.93)^x<100000 so the answer is 23 becuase 100000/50000000 is about 0.02 and 0.02 is greater then 0.93^23 and the answer is \(23\)