1. The graph below shows the concentration of a drug (in mg/L) in the bloodstream, t hours after it is taken orally. Use the graph to answer a-f. AY 80 a. What is the concentration after 8 hours? 76 72 b. Over what interval(s) does the concentration increase? Over what interval(s) does the concentration decrease? 68 64 60 56 c. When is the drug at its maximum concentration? What is the maximum concentration of the drug? 52 48 44 40 d. After the drug reaches its maximum concentration, how many hours are required for the concentration to decrease to 16 mg/L? 36 32 28- 24 20 e. What does the graph predict about the 16 concentration after 1 week? After 1 month? 12 f. Summarize the concentration of the drug in the bloodstream for the first 20 hours after it is taken. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Use findings from a-e to validate your statements.

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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**1. The graph below shows the concentration of a drug (in mg/L) in the bloodstream, t hours after it is taken orally. Use the graph to answer questions a-f.**

The graph illustrates a curve representing the drug concentration over time, starting at the origin, peaking, and then decreasing gradually. The x-axis represents time in hours, ranging from 0 to 20, while the y-axis represents concentration in mg/L, ranging from 0 to 80.

- **a. What is the concentration after 8 hours?**

- **b. Over what interval(s) does the concentration increase? Over what interval(s) does the concentration decrease?**

- **c. When is the drug at its maximum concentration? What is the maximum concentration of the drug?**

- **d. After the drug reaches its maximum concentration, how many hours are required for the concentration to decrease to 16 mg/L?**

- **e. What does the graph predict about the concentration after 1 week? After 1 month?**

- **f. 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.**

**2. Suppose another drug is administered intravenously. The concentration c of the drug (in mg/L) in the bloodstream, t hours after it is administered, is modeled by the function \(c(t) = \frac{20t}{t^2 + 4}\).**

- **a. Determine when the concentration will be 0.5 mg/L.**

- **b. Complete the table representing the concentration of the drug in the bloodstream, t hours after administration. Round to two decimal places as needed.**

  | t  | 0  | 2  | 4  | 6  | 8  | 10 | 12 | 14 | 16 | 18 | 20 |
  |----|----|----|----|----|----|----|----|----|----|----|----|
  | c(t)|    |    |    |    |    |    |    |    |    |    |    |

- **c. What is a reasonable domain for this function? Justify your answer.**

- **d. When must the patient receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below
Transcribed Image Text:**1. The graph below shows the concentration of a drug (in mg/L) in the bloodstream, t hours after it is taken orally. Use the graph to answer questions a-f.** The graph illustrates a curve representing the drug concentration over time, starting at the origin, peaking, and then decreasing gradually. The x-axis represents time in hours, ranging from 0 to 20, while the y-axis represents concentration in mg/L, ranging from 0 to 80. - **a. What is the concentration after 8 hours?** - **b. Over what interval(s) does the concentration increase? Over what interval(s) does the concentration decrease?** - **c. When is the drug at its maximum concentration? What is the maximum concentration of the drug?** - **d. After the drug reaches its maximum concentration, how many hours are required for the concentration to decrease to 16 mg/L?** - **e. What does the graph predict about the concentration after 1 week? After 1 month?** - **f. 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.** **2. Suppose another drug is administered intravenously. The concentration c of the drug (in mg/L) in the bloodstream, t hours after it is administered, is modeled by the function \(c(t) = \frac{20t}{t^2 + 4}\).** - **a. Determine when the concentration will be 0.5 mg/L.** - **b. Complete the table representing the concentration of the drug in the bloodstream, t hours after administration. Round to two decimal places as needed.** | t | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | |----|----|----|----|----|----|----|----|----|----|----|----| | c(t)| | | | | | | | | | | | - **c. What is a reasonable domain for this function? Justify your answer.** - **d. When must the patient receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below
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