The concentration C (in milligrams per milliliter) of a drug in a patient's bloodstream t hours after injection into muscle tissue is modeled by
C =
3t/26 + t^3
Use differentials to approximate the change in the concentration when t changes from
t = 1
to
t = 1.5.
(Round your answer to four decimal places.)
see your other problem as an example. if necessary, I can check your work.
hey bobpursley i tried this one on my own but i don't get the right answer i mean if u can give me the solution i will look at it thanks
0.04938
To approximate the change in concentration (ΔC) when t changes from 1 to 1.5, we can use differentials.
First, let's find the derivative of the concentration function C(t) with respect to t. Differentiating the equation C = 3t/26 + t^3 gives us:
dC/dt = (3/26) + 3t^2
Now, we can use differentials to approximate the change in concentration. The differential form is as follows:
dC = (dC/dt) * dt
Substituting the given values t = 1 and dt = 1.5 - 1 = 0.5 into the equation, we get:
dC = [(3/26) + 3(1)^2] * 0.5
dC = (3/26) + 3 * 0.5
Calculating this approximation:
dC ≈ (3/26) + 1.5 ≈ 0.6538
Therefore, the approximate change in concentration when t changes from 1 to 1.5 is approximately 0.6538 milligrams per milliliter.