SOLUTION: In testing the effects of a drug, the percentage of the drug in the blood stream was given by p = 0.090t – 0.015t^2, where t is the time (in hours) after the drug was administered.

Algebra ->  Permutations -> SOLUTION: In testing the effects of a drug, the percentage of the drug in the blood stream was given by p = 0.090t – 0.015t^2, where t is the time (in hours) after the drug was administered.      Log On


   

Question 869603: In testing the effects of a drug, the percentage of the drug in the blood stream was given by p = 0.090t – 0.015t^2, where t is the time (in hours) after the drug was administered.
a. What is the maximum number of hours that the drug is in blood?
b. How much of the drug is in the system after 15 minutes?
c. How long is at least 12 percent of the drug in the system?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)Find t when p=0.
0.090t-0.015t%5E2=0
0.090t=0.015t%5E2
t=0.090%2F0.015
t=6 hours
b) 15 minutes = 1/4 hour
p=0.090%281%2F4%29-0.015%281%2F16%29
p=0.0225-.0009375
p=0.0215625
c) graph%28300%2C300%2C-2%2C8%2C-1%2C2%2C0.090x-0.015x%5E2%29
Looks for the two points when p=0.12
0.090t-0.015t%5E2=0.12
-15t%5E2%2B90t-120=0
t%5E2-6t%2B8=0
%28t-2%29%28t-4%29=0
Two solutions: t=2 and t=4
So the difference is how long the drug is above 12%.
DELTA=4-2=2hours