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) 0.33 0.24 0.18 0.12 0.07

(a) Find the average change of C with respect to t over each time interval.

Answer 1

The average change of C will be
`Average\ change=(C(t_(2))-C(t_(1)))/(t_(2)-t_(1))`.

Explanation:

The data provided is:

t: 1.0 | 1.5 | 2.0 | 2.5 | 3.0

C (t): 0.33 | 0.24 | 0.18 | 0.12 | 0.07

The average change of C will be compute using the formula:

`Average\ change=(C(t_(2))-C(t_(1)))/(t_(2)-t_(1))`

For example, let's compute the average change of C w.r.t. t over the interval [1.0, 2.0] as follows:

`Average\ change=(C(2.0)-C(1.0))/(2.0-1.0)=(0.18-0.33)/(1)=-0.15`

Consider another example, compute the average change of C w.r.t. t over the interval [1.5, 2.5] as follows:

`Average\ change=(C(2.5)-C(1.5))/(2.5-1.5)=(0.12-0.24)/(1)=-0.12`