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.) t (hours) 1.0 1.5 2.0 2.5 3.0 c(t) (mg/ml) 0.31 0.22 0.16 0.1 0.06 (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? H ml/mg h mg/ml h h mg/ml mg/ml ml/mg h

Answer 1

Answer:

a)

i) at [1.0,2.0] = = -0.15 mg/ml¬hr

ii) at [1.5, 2.0]  = - 0.12 mg/ml¬hr

iii) at [2.0, 2.5] = -0.12  mg/ml¬hr

(iv) at [2.0, 3.0] = -0.1 mg/ml¬hr

b) the instantaneous rate of change at t = 2 = 0.12  mg/ml¬hr and the unit will be h mg /ml

Explanation:

1) according to the table of the change in c (mg/ml) and the change in time (hours) So, we are going to use this formula to solve part (a)

m = ΔC / Δt

when m is the average change of c with respect to t over each time interval

i) [1.0,2.0] :

m = ΔC / Δt

   = (0.16-0.31)/(2-1)

   = -0.15 mg/ml¬hr

ii) [1.5, 2.0]:

m = ΔC / Δt

    = (0.16-0.22)/(2-1.5)

    = - 0.12 mg/ml¬hr

iii) [2.0, 2.5]:

m = ΔC / Δt

    = (0.1 - 0.16)/(2.5-2)

    =  -0.12  mg/ml¬hr

(iv) [2.0, 3.0] :

m = ΔC / Δt

   = (0.06-0.16)/(3-2)

   = -0.1 mg/ml¬hr

(b) to estimate the instantaneous rate of change at t = 2 we can see the results at (ii) and (iii) at time rates [1.5, 2.0] and [2.0, 2.5] both are the same answer = -0.12 mg/ml¬hr so, the instantaneous rate of change at t=2 is equal -0.12 and the unit will be h mg/ml because (mg/ml) / h = mg h /ml

Answer 2

The study of chemicals and bonds is called chemistry.

The correct answer to the question is a)

i) at [1.0,2.0] = = -0.15 mg/ml¬hr

ii) at [1.5, 2.0]  = - 0.12 mg/ml¬hr

iii) at [2.0, 2.5] = -0.12  mg/ml¬hr

(iv) at [2.0, 3.0] = -0.1 mg/ml¬hr

and

b) the instantaneous rate of change at t = 2 = 0.12  mg/ml¬hr and the unit will be h mg /ml

What is alcohol?

• An alcoholic drink is a drink that contains ethanol, a type of alcohol produced by the fermentation of grains, fruits, or other sources of sugar that acts like a drug.
• The consumption of alcoholic drinks often referred to as "drinking", plays an important social role in many cultures.

1) according to the table of the change in c (mg/ml) and the change in time (hours), we are going to use this formula to solve part (a)

m = ΔC / Δt

when m is the average change of c with respect to t over each time interval

i) [1.0,2.0] :

m = ΔC / Δt

  = (0.16-0.31)/(2-1)

  = -0.15 mg/ml¬hr

ii) [1.5, 2.0]:

m = ΔC / Δt

   = (0.16-0.22)/(2-1.5)

   = - 0.12 mg/ml¬hr

iii) [2.0, 2.5]:

m = ΔC / Δt

   = (0.1 - 0.16)/(2.5-2)

   =  -0.12  mg/ml¬hr

(iv) [2.0, 3.0] :

m = ΔC / Δt

  = (0.06-0.16)/(3-2)

  = -0.1 mg/ml¬hr

(b) to estimate the instantaneous rate of change at t = 2 we can see the results at (ii) and (iii) at time rates [1.5, 2.0] and [2.0, 2.5] both are the same answer = -0.12 mg/ml¬hr so, the instantaneous rate of change at t=2 is equal -0.12 and the unit will be h mg/ml because (mg/ml) / h = mg h /ml

Hence, the correct answer to the mentioned above.

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