Question

i ori A artada, paintele r med ne has a decay rae o 19% per hour Apatent was iven a dose of the medi ne 6 hours a and there s currenty 82 mlgan sof the medicine n the misgrams After the dose was given how long must the patent wat for there to be less than 25% of the oniginal dose of the medicine let in his or her bloodstream? Express your answer as a decimal to the nearest tenth

Answer 1

solution:-

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

===> Ao= 297.4504 mg

the requirement is to assess number of hours to be required to reduce the medicine to 25% of the original dose i.e. 25% of Ao= 297.4504 mg i.e. 76.3626 mg.

Let us assume it would require y hours.

Then, A(y)= Ao(1-r)^y

76.3626= 297.4504 * 0.81^y

0.81^y= 0.25

y= ln 0.25 / ln 0.81= 6.58 = 6.6 (nearest tenth of an hour)