When will the concentration of the drug fall to a level of 0.5 mg/L?, math homework help

Anonymous

Question Description

7. Suppose that another drug is administered intravenously to an adult patient in a hospital as prescribed by a doctor. The relationship between the concentration of the drug (in mg/L) in the bloodstream and the time (in hours after administration) is modeled by the function.

a) Using the function above, fill in a chart of the concentration of the drug in the bloodstream for the first 24-hour period after administration at intervals of two hours. Write the concentration accurate to two decimal places as needed.

 t 0 2 4 6 8 10 12 14 16 18 20 22 24 c(t)

b) When will the concentration of the drug fall to a level of 0.5 mg/L?

c) When must the next dose of the drug be administered to the patient in order to maintain a concentration above 1 mg/L and below 8 mg/L? Explain your reasoning.

d) What is a reasonable domain for this function? Justify why (and if) you would exclude any values.

Borys_S
School: Rice University

The solutions are ready.The question c is not that simple. Do you know derivatives?

20t
.
t ļ«4
2

a. The chart.
t

0

2

4

6

8

10

12

14

16

18

20

22

24

c(t) 0.00 5.00 4.00 3.00 2.35 1.92 1.62 1.40 1.23 1.10 0.99 0.90 0.83

b. The concentration will fall to 0.5 mg/L for š” > 24 such that

20š”
š” 2 +4

= 0.5. It is the same as

40š” = š” 2 + 4, or š” 2 ā 40š” + 4 = 0. The root in question is š” = 20 + ā202 ā 4 ā šš. š (hours).
c. Using the table: the concentration drops below 1 mg/L after about 20 h...

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