26 Lidocaine is a drug used to treat irregular heartbeats. After an injection of a 100-mg dose of lidocaine, the amount of the drug in a patient's bloodstream is33.67(e 0.0075731t - e-0.12043) mgat time t minutes after the injection.(a) Make a graph of the amount of drug in the bloodstream for t up to 4 hours (240 minutes).yy3025025200201501510010505010015020050100150200y3015025201001510505010015020050100150200(b) When does the drug reach its maximum level in the bloodstream? (Round your answer to two decimal places.)min(c) For a person of typical size, the drug is effective as long as the amount in the bloodstream is at least 7.5 mg. For how long is the drug at or above that level? (Hint: The drug is at that level twice. Round your answer to two decimal places.)min(d) For a person of typical size, the lethal level is when the amount in the bloodstream exceeds 30 mg. Is this dose lethal for such a person?O VesO No(e) For a small person, the lethal level is when the amount in the bloodstream exceeds 20 mg. Is this dose lethal for such a person?O YesO NoIf so, after how many minutes will it be lethal? (If the dose is not lethal, enter NOT LETHAL.)min

Name: 26 Lidocaine is a drug used to treat irregular heartbeats. After an in
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Description: 26 Lidocaine is a drug used to treat irregular heartbeats. After an injection of a 100-mg dose of lidocaine, the amount of the drug in a patient's bloodstream is33.67(e 0.0075731t - e-0.12043) mgat time t minutes after the injection.(a) Make a graph

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Lidocaine is a drug used to treat irregular heartbeats. After an injection of a 100-mg dose of lidocaine, the amount of the drug in a patient's bloodstream is
33.67(e 0.0075731t - e-0.12043) mg
at time t minutes after the injection.
(a) Make a graph of the amount of drug in the bloodstream for t up to 4 hours (240 minutes).
y
y
30
250
25
200
20
150
15
100
10
50
50
100
150
200
50
100
150
200
y
30
150
25
20
100
15
10
50
50
100
150
200
50
100
150
200
(b) When does the drug reach its maximum level in the bloodstream? (Round your answer to two decimal places.)
min
(c) For a person of typical size, the drug is effective as long as the amount in the bloodstream is at least 7.5 mg. For how long is the drug at or above that level? (Hint: The drug is at that level twice. Round your answer to two decimal places.)
min
(d) For a person of typical size, the lethal level is when the amount in the bloodstream exceeds 30 mg. Is this dose lethal for such a person?
O Ves
O No
(e) For a small person, the lethal level is when the amount in the bloodstream exceeds 20 mg. Is this dose lethal for such a person?
O Yes
O No
If so, after how many minutes will it be lethal? (If the dose is not lethal, enter NOT LETHAL.)
min

Expert Solution

Step 1

For the first option, enter the function, $f (t) = 33.67 (e^{- 0.0075731 t} - e^{- 0.12043 t})$ in any graphing utility to obtain the graph.

For the second option, find the maximum value of $f (t)$ on the graph.

For the third option, substitute $f (t) = 7.5$ in the equation $f (t) = 33.67 (e^{- 0.0075731 t} - e^{- 0.12043 t})$ and solve for $t$ .

For the last option, find the value of $t$ at which the line $f (t) = 20$ crosses the graph of $f (t) = 33.67 (e^{- 0.0075731 t} - e^{- 0.12043 t})$ for the first time.

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