When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream after t minutes is given by?

[匿名]

2016-07-13 3:47 pm

C(t) = 0.08t − 0.0004t2,
where 0 ≤ t ≤ 240 and the concentration is measured in mg/L.

When is the maximum serum concentration reached? t=?min?
What is the maximum concentration? in mg/L?

Please include steps if possible , thanks!

回答 (2)

不用客氣

2016-07-13 4:06 pm

✔ 最佳答案

Method 1 : Differentiation

C(t) = 0.08t - 0.0004t²
C'(t) = 0.08 - 0.0008t
C"(t) = -0.0008

When C'(t) = 0 :
0.08 - 0.0008t = 0
0.0008t = 0.08
t = 100
Hence, maximum concentration = 4 mg/L
at time = 100 min

====
Method 2 : Completing square

C(t) = 0.08t - 0.0004t²
C(t) = -0.0004[t² - 200t]
C(t) = -0.0004[t² - 2(100)t + 100²] + 0.0004*100²
C(t) = -0.0004(t - 100)² + 4

For all real t, -0.0004(t - 100)² ≤ 0
Hence, C(t) = -0.0004(t - 100)² + 4 ≤ 0

Maximum C(t) = 4

When C(t) = 4 :
-0.0004(t - 100)²
t = 100

Hence, maximum concentration = 4 mg/L
at time = 100 min

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[匿名]

2016-07-13 4:05 pm

Just learn derivatives....

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