A particular pain relieving medicine has a decay rate of 19% per hour. A patient

Question

A particular pain relieving medicine has a decay rate of 19% per hour. A patient was given a dose of the medicine 4 hours ago and there is currently 80 milligrams of the medicine in the patients bloodstream. What was the original dose of the medicine? ______ milligrams After the dose was given how long must the patient wait for there to be less than 25% of the original dose of the medicine left in his or her bloodstream? Express your answer as a decimal to the nearest tenth of an hour. _________ hours

Explanation / Answer

since decay rate is 19% that is 0.19 of original amount =0.19A

so amount left is A-0.19A =0.81A

So amount left after x hours,y =A(0.81)^x

a)

y=80 and x=4

80 = A (0.81)^4

A =80/(0.81)^4

=185.8

b)

y =185.8(0.81)^x

25% of original amount means 0.25*185.8 =46.45

so y =46.45

and we have to find x

46.45 = 185.8(0.81)^x

46.45/185.8 =(0.81)^x

0.25 = (0.81)^x

log(0.25) = xlog(0.81)

x=log(0.25)/log(0.81)

= 6.6 hours

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