The quantity Q(t) of a drug in the bloodstream, in mg, at hour t, decays exponentially, as given in the graph and the table below. Assume the pattern in the table holds. Complete parts (a) through (d) below. (a) Fill in the table. Hint: Some of the values are listed on the vertical axis. (Type an integer or decimal rounded to one decimal place as needed.) Amount Q, Time, t, (hours) 102.47 (mg) Number 3 102.4 6. 51.2 9. 25.6 12 12.8 51.2- 15 2.274 18 .8503 25.6- 6 9. 12 15 18 21 24 (b) Report the half-life. Use the pull-down menu to report the units. The half-life is 37 hours (c) Write a formula which gives Q as a function of t. The parameters in the formula should not contain rounded values. Include 0.5 in your formula. Q = ABP (Your answer involves 0.5, real numbers, and a lower case t.) TIP: If desired, click on the Plot icon ( F) next to the answer box to graph your response. (Although your answer may match the graph, it will be counted incorrect if it is not in the form requested.) (d) Estimate the length of time until the amount of the drug in the patient's bloodstream is 0.4 mg. After Number hours, the amount of drug in the bloodstream is 0.4 mg. (Type an integer or decimal rounded to one decimal place as needed.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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b-d

The quantity Q(t) of a drug in the bloodstream, in mg, at hour t, decays exponentially, as given in the graph and the table
below. Assume the pattern in the table holds.
Complete parts (a) through (d) below.
(a) Fill in the table. Hint: Some of the values are listed on the vertical axis.
(Type an integer or decimal rounded to one decimal place as needed.)
Amount Q,
102.47
Time, t, (hours)
(mg)
Number
3
102.4
51.2
9
25.6
12
12.8
51.2-
15
2.274
18
.8503
25.6-
3
6
12
15
18
21
24
(b) Report the half-life. Use the pull-down menu to report the units.
The half-life is 37
hours
(c) Write a formula which gives Q as a function of t.
The parameters in the formula should not contain rounded values. Include 0.5 in your formula.
Q =
OEE (Your answer involves 0.5, real numbers, and a lower case t.)
TIP: If desired, click on the Plot icon () next to the answer box to graph your response.
(Although your answer may match the graph, it will be counted incorrect if it is not in the form requested.)
(d) Estimate the length of time until the amount of the drug in the patient's bloodstream is 0.4 mg.
After
Number
hours, the amount of drug in the bloodstream is 0.4 mg.
(Type an integer or decimal rounded to one decimal place as needed.)
Transcribed Image Text:The quantity Q(t) of a drug in the bloodstream, in mg, at hour t, decays exponentially, as given in the graph and the table below. Assume the pattern in the table holds. Complete parts (a) through (d) below. (a) Fill in the table. Hint: Some of the values are listed on the vertical axis. (Type an integer or decimal rounded to one decimal place as needed.) Amount Q, 102.47 Time, t, (hours) (mg) Number 3 102.4 51.2 9 25.6 12 12.8 51.2- 15 2.274 18 .8503 25.6- 3 6 12 15 18 21 24 (b) Report the half-life. Use the pull-down menu to report the units. The half-life is 37 hours (c) Write a formula which gives Q as a function of t. The parameters in the formula should not contain rounded values. Include 0.5 in your formula. Q = OEE (Your answer involves 0.5, real numbers, and a lower case t.) TIP: If desired, click on the Plot icon () next to the answer box to graph your response. (Although your answer may match the graph, it will be counted incorrect if it is not in the form requested.) (d) Estimate the length of time until the amount of the drug in the patient's bloodstream is 0.4 mg. After Number hours, the amount of drug in the bloodstream is 0.4 mg. (Type an integer or decimal rounded to one decimal place as needed.)
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