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) 0.33 0.22 0.16 0.1 0.09 (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 h ml/mg ml/mg h mg/ml h mg/ml mg/ml h

a) Average change over each time interval: see below

b) Instantaneous rate of change at t = 2: - 0.12 mg/mL/h

   Units are: mg/mL/h or mg/(mL . h), they are equivalen.

Explanation:

         t (hours)         1.0       1.5         2.0      2.5      3.0

        C(t) (mg/mL)   0.33     0.22    0.16      0.1       0.09

a) Average rate of change:

     Interval            Rate of change (mg/mL / h)

(i) [1.0, 1.5]              [0.22 - 0.33] / [1.5 - 1.0] = - 0.22

(ii) [1.5, 2.0]             [0.16 - 0.22] / [2.0 - 1.5] = - 0.12

(iii) [2.0, 2.5]           [0.1 - 0.16] / [2.5 - 2.0] = - 0.12

(iv) [2.0, 3.0]           [0.09 - 0.1] / [3.0 - 2.5] = - 0.02

b) Estimation of the instantaneous rate of change at t = 2.

You obtain the units by dividing the units of the numerator (mg/mL) by the units of the denominator (h). This is how you obtain them:

it is the most commonly accepted one