When a certain prescription drug is taken orally by an adult, the amount of the

Question

When a certain prescription drug is taken orally by an adult, the amount of the drug (in mg/L) in the bloodstream at t hours is given by the function y = f(t) shown in the graph. 1) What is the concentration of the drug in the bloodstream at t = 8 hours? 2) During what time interval is the drug level in the bloodstream increasing? Decreasing? 3) When does the level of the drug in the bloodstream reach its maximum value, and what is the concentration in the bloodstream at that time? 4) After the drug reaches its maximum level in the bloodstream, how many additional hours are required for the level to drop to 16 mg/L? 5) As time increases, what does the graph predict about the level of the drug in the bloodstream? 6) In 3 4 sentences, summarize what happens to the amount of drugs in the system in the first 20 hours. Use numerical findings from #1 5 to validate your statements 80t--r -r r 76 -------i--+------- 72 56 14L------ L J- 1 -L J- L- 48 40 24 16 8 9 10 11 12 13 14 15 16 17 18 19 20

Explanation / Answer

Solution:

(1). the concentration of the drug in the bloodstream at t = 8 hours

y(8) = 16  mg/L

(2)As we can see that graph is increasing up to t = 2 sec

and t = 2 slope of graph = 0

ie concentration neither increasing and decreasing at t = 2

therefore Increasing interval = ( 0, 2)

and decreasing interval = (2,)

(3).

the level of the drug in the bloodstream reach its maximum value at t = 2 sec, and the concentration in the bloodstream at that time = 64 mg/l

(4) After the drug reaches its maximum level in the bloodstream, it takes 8 more additional hours are required for the level to drop to 16 mg/L ( g(10) = 16 mg/L )

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