The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is given by the following. 7t t20 27 +³ (a) Complete the table and use it to approximate the time when the concentration is greatest. (Round your answers to three decimal places.) 0 0.5 2 2.5 3 C(t) = t C(t) 0 O 1.3 C(t) 1.2 cm 1.1 t 2.5 (b) Use a graphing utility to graph the concentration function and use the graph to approximate the time when the concentration is the greatest. 1.4 0.4 0.3 0 ✓ ✔hr 0.5 0.129 ✔ 0.250 1 1.5 1 2 2.5 0.346 O 1.4 1.5 1.3- C) 1.2 CT) 0.2 0 0.3- ✓0.4000 ✔ 0.411 ✓ 0.389 0.5 1 1.5 1 2 2.5 3

College Algebra
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Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
Problem 56E: When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream...
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The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is given by the following.
7t
27 + +3'
(a) Complete the table and use it to approximate the time when the concentration is greatest. (Round your answers to three decimal places.)
0
0.5
1
2
3
C(t) =
t≈ 2.5
t
C(t) 0
1.4
1.3-
C(1) 1.2-
1.1-
1-
0 0.5
0.4-
t> 0
0.3-
C(t) 0.2-
hr
(b) Use a graphing utility to graph the concentration function and use the graph to approximate the time when the concentration is the greatest.
0.129
1
1.5
t
0.250
2
2.5
0.346
O
1.5
1.4
1.3-
C(1) 1.2-
1.1-
0.4-
0.4000
0.5
0.3-
1
Cr
C(1) 0.2
1.5
t
0.411
2
2.5
2.5
0.389
3
►
Transcribed Image Text:The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is given by the following. 7t 27 + +3' (a) Complete the table and use it to approximate the time when the concentration is greatest. (Round your answers to three decimal places.) 0 0.5 1 2 3 C(t) = t≈ 2.5 t C(t) 0 1.4 1.3- C(1) 1.2- 1.1- 1- 0 0.5 0.4- t> 0 0.3- C(t) 0.2- hr (b) Use a graphing utility to graph the concentration function and use the graph to approximate the time when the concentration is the greatest. 0.129 1 1.5 t 0.250 2 2.5 0.346 O 1.5 1.4 1.3- C(1) 1.2- 1.1- 0.4- 0.4000 0.5 0.3- 1 Cr C(1) 0.2 1.5 t 0.411 2 2.5 2.5 0.389 3 ►
t≈ 2.3811
0
0.4
0.3-
C(t) 0.2-
0.5
0.1-
0.5
1
hr
X
1.5
t
1
2
0.4
0.3-
C(t) 0.2-
LD
0.1-
0
2.5
1.5
t
2.5
2
3
O
0 0.5
1
0.5
1.5
t
1
1.5
(c) Use calculus to determine analytically the time when the concentration is greatest.
t = 2
hr
2
t
2.5
2
2.5
3
3
Transcribed Image Text:t≈ 2.3811 0 0.4 0.3- C(t) 0.2- 0.5 0.1- 0.5 1 hr X 1.5 t 1 2 0.4 0.3- C(t) 0.2- LD 0.1- 0 2.5 1.5 t 2.5 2 3 O 0 0.5 1 0.5 1.5 t 1 1.5 (c) Use calculus to determine analytically the time when the concentration is greatest. t = 2 hr 2 t 2.5 2 2.5 3 3
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