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

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

in chemistry, adhesion and cohesion are attractive forces that exist between molecules. they hold the molecules together from each other. they are different in that adhesive force exists between molecules of different substance while cohesive force happens between molecules of same substance.

adhesion between water and glass causes water molecules at the edge of water and glass interface to climb up the wall in a narrow glass tube. this is called capillary action. cohesion is what gives glass its shape and causes water to form a droplet.