A drug is injected into a patient's bloodstream. The concentration of the drug in the bloodstream t hours after the drug is injected is modeled by the formula C(t)= .12t/(t^2+t+1) miligrams per cubic centimeter. Estimate the change in concentration over the time period from 30 to 35 minutes after injection

So i took the derivative got ((t^2+t+1)(.12)-(2t+1)(.12t))/(t^2+t+1)^2

Plugged in .5 into the derivative and multiplied that by 5/60 (5minutes change in time) ended up with .00244898 and webwork says I'm wrong.

Anyone know what I did wrong?

Question

A drug is injected into a patient's bloodstream. The concentration of the drug in the bloodstream t hours after the drug is injected is modeled by the formula C(t)= .12t/(t^2+t+1) miligrams per cubic centimeter. Estimate the change in concentration over the time period from 30 to 35 minutes after injection

So i took the derivative got ((t^2+t+1)(.12)-(2t+1)(.12t))/(t^2+t+1)^2

Plugged in .5 into the derivative and multiplied that by 5/60 (5minutes change in time) ended up with .00244898 and webwork says I'm wrong.

Anyone know what I did wrong?

tkhunny · Answer

Three possibilities come to mind:

1) Why not calculate it directly?  C(35/60) - C(30/60)?
2) Why is C'(30/60) preferable to C'(35/60)?  Are they the same?  An average o fthe two may be a more rational approximation.
3) Negative, perhaps?

anonymous · Answer

Thanks for suggestion 3)!! I was right except the answer was negative (-0.00244898)