Submission Instructions: 1. All explanations must be typed. Supporting math work must be neat, written by hand, and suitable for copying or scanning.

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• Use the heading βGEN ED ASSESSMENT:β on the assignment.
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1. The graph below shows the concentration of a drug (in mg/L) in the bloodstream, π‘ hours after it is taken orally. Use the graph to answer a-f.
1. What is the concentration after 8 hours?                                                   24 mg/L of concentration after 8 hours have passed
• Over what interval(s) does the concentration increase?                                                                                    Over what interval(s) does the concentration decrease?                                                                                                       the time span during which concentration rises is [0 to 8] hours                                                                                                     the time span during which concentration decreases is [8 to 80] hours

c. When is the drug at its maximum concentration? What is the maximum concentration of the drug?                                 After 8 hours, the drug’s highest content is 64 mg/L. 64 mg/L is the maximum concentration.

• Time = 8 hours later
• After the drug reaches its maximum concentration, how many hours are required for the concentration to decrease to 16 mg/L?                                                                          After the drug achieves its highest concentration, it takes 40 hours for the concentration to drop to 16 mg/L. 40 hours are required to achieve a quantity of 16 mg/L.
• What does the graph predict about the concentration after 1 week? After 1 month? According to the image, drug concentration will remain consistent after another week but then after one 30 days as well, with concentration dropping after eight hours and stabilizing.
• Summarize the concentration of the drug in the bloodstream for the first 20 hours after it is taken. Use findings from a-e to validate your statements.                        the drug’s plasma levels for the first 20 hours. Internally, focus rises for the first 0 to 8 hours. The peak concentration is reached after 8 hours of concentration. Following that, focus begins to decline.
• Suppose another drug is administered intravenously. The concentration π of the drug (in mg/L) in the

bloodstream, π‘ hours after it is administered, is modeled by the function c(t)=20t/t^2+4

1. Determine when the concentration will be 0.5 mg/L.
• Complete the table representing the concentration of the drug in the bloodstream, π‘ hours after administration.  Round to two decimal places as needed.
• What is a reasonable domain for this function? Justify your answer.                                                                                            Given that the drug concentration is o at t=0 and that it never truly becomes zero for any t where t0, a sensible scope is (t0). There is a quantity c at any moment, where C0.
• When must the patient receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L?  Explain your reasoning.                                                               A quantity of between 1 mg/L and 88 mg/c.  When t=20 min, C(t) equals 1 mg/c [see table]. C(t)=8=) 8=20t/t2+4 translates to 8t2-20t+32=0 and t=1.25 minutes. In order to maintain a quantity between 1 mg/c and 8 mg/c, the medication must be given between time t where (1.25 min t 20 min).
• Compare the concentration of the oral drug (#1) and the concentration of the intravenous drug (#2) over the first 20 hours after it is given.

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