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Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour after consumption of 30 mL ethanol (corresponding to two alcoholic drinks). Selected values of C(t) are given in the table. (Round your answers to two decimal places.) t (hours) 1.0 1.5 2.0 2.5 3.0 C(t) (g/dL) 0.33 0.22 0.16 0.1 0.05 (a) Find the average change of C with respect to t over each time interval. (1) [1.0, 2.0] (ii) [1.5, 2.0] (iii) [2.0, 2.5] (iv) [2.0, 3.0] (b) Estimate the instantaneous rate of change at t = 2 and interpret your result. What are the units? h g/dL g/dL g/dL h dL/g h h dL/9

Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour after consumption of 30 mL ethanol (corresponding to two alcoholic drinks). Selected values of C(t) are given in the table. (Round your answers to two decimal places.) t (hours) 1.0 1.5 2.0 2.5 3.0 C(t) (g/dL) 0.33 0.22 0.16 0.1 0.05 (a) Find the average change of C with respect to t over each time interval. (1) [1.0, 2.0] (ii) [1.5, 2.0] (iii) [2.0, 2.5] (iv) [2.0, 3.0] (b) Estimate the instantaneous rate of change at t = 2 and interpret your result. What are the units? h g/dL g/dL g/dL h dL/g h h dL/9

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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour after consumption of 30 mL of ethanol (corresponding to two alcoholic drinks). Selected values of C(t) are given in the table. (Round your answers to two decimal places.) t (hours) 1.0 1.5 2.0 C(t) (g/dL) 0.33 0.22 0.16 (ii) [1.5, 2.0] (a) Find the average change of C with respect to t over each time interval. (i) [1.0, 2.0] (iii) [2.0, 2.5] (iv) [2.0, 3.0] What are the units? h g/dL g/dL g/dL h (b) Estimate the instantaneous rate of change at t = 2 and interpret your result. dL/g h 3.0 0.1 0.05 h 2.5 h dL/g
Transcribed Image Text:Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour after consumption of 30 mL of ethanol (corresponding to two alcoholic drinks). Selected values of C(t) are given in the table. (Round your answers to two decimal places.) t (hours) 1.0 1.5 2.0 C(t) (g/dL) 0.33 0.22 0.16 (ii) [1.5, 2.0] (a) Find the average change of C with respect to t over each time interval. (i) [1.0, 2.0] (iii) [2.0, 2.5] (iv) [2.0, 3.0] What are the units? h g/dL g/dL g/dL h (b) Estimate the instantaneous rate of change at t = 2 and interpret your result. dL/g h 3.0 0.1 0.05 h 2.5 h dL/g
Expert Solution
Step 1

(a)

(i) time interval = [1.0, 2.0]

Average change of C = concentraion at (2.0) - concentration at (1.0)2.0-1.0 = 0.16-0.331.30

∴ Average change of C = - 0.17

 

(ii) time interval = [1.5, 2.0]

Average change of C = concentraion at (2.0) - concentration at (1.5)2.0-1.5 = 0.16-0.220.5

∴ Average change of C = - 0.12

 

(iii) time interval = [2.0, 2.5]

Average change of C = concentraion at (2.5) - concentration at (2.0)2.5-2.0 = 0.1-0.160.5

∴ Average change of C = - 0.12

 

(iv) time interval = [2.0, 3.0]

Average change of C = concentraion at (3.0) - concentration at (2.0)2.0-1.0 = 0.06-0.161.00

∴ Average change of C = - 0.10

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