Researchers measured the average blood alcohol concentration C ( t ) of eight me
ID: 2894654 • Letter: R
Question
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). (Round your answers to two decimal places.)
(a) Find the average change of C with respect to t over each time interval.
(i) [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.
What are the units?
mg/mL
h
t (hours) 1.0 1.5 2.0 2.5 3.0 C(t) (mg/mL) 0.33 0.22 0.16 0.1 0.06Explanation / Answer
(i) [1.0, 2.0]
average change of C with respect to t =[C(2.0)-C(1.0)]/(2.0-1.0)
average change of C with respect to t =[0.16-0.33]/(1.0)
average change of C with respect to t =-0.17 (mg/mL)/h
(ii) [1.5, 2.0]
average change of C with respect to t =[C(2.0)-C(1.5)]/(2.0-1.5)
average change of C with respect to t =[0.16-0.22]/(0.5)
average change of C with respect to t =-0.12 (mg/mL)/h
(iii) [2.0, 2.5]
average change of C with respect to t =[C(2.5)-C(2.0)]/(2.5-2.0)
average change of C with respect to t =[0.1-0.16]/(0.5)
average change of C with respect to t =-0.12 (mg/mL)/h
(iv) [2.0, 3.0]
average change of C with respect to t =[C(3.0)-C(2.0)]/(3.0-2.0)
average change of C with respect to t =[0.06-0.16]/(1.0)
average change of C with respect to t =-0.10 (mg/mL)/h
(b) the instantaneous rate of change at t = 2 is =-0.12 (mg/mL)/h
units are (mg/mL)/h
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