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# 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

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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?

Jun 9, 2020

#1
+1

100,000 =50,000,000 * 0.93^n
Divide both sides by 50,000,000
0.002 =0.93^n

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.

Jun 9, 2020
#2
+1128
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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 \(23\)

Jun 9, 2020
edited by jimkey17  Jun 9, 2020
#3
+26605
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Well, first of all    100 000 / 50 000 000  = =   . 00 2

so  .002 > .9386.63523174

so x = 85.635     TIME periods     each period is six hours

* 6 = 513 .81 hours = 21.4 days

ElectricPavlov  Jun 9, 2020