The average blood alcohol concentration (bac) of eight male subjects was measured after consumption of 15 ml of ethanol (corresponding to one alcoholic drink). the resulting data were modeled by the concentration function c(t) = 0.0225te−0.0467t where t is measured in minutes after consumption and c is measured in mg/ml. (round your answers to five decimal places.) (a) how rapidly was the bac increasing after 9 minutes? (mg/ml)/min (b) how rapidly was it decreasing half an hour later (t = 30)? (mg/ml)/min

Explanation:

The function that modeled the data is:

Since you need to determine how rapidly the concentrations will vary (increase or decrease) at different times, this is the instantaneous speed or rate of change, you need to find the first derivative of C(t), C'(t)

The next steps show the use of the rule of chain to find C'(t):

Now that you have the expression for the speed at which the concentration changes, you just need to substitute the values.

(a) How rapidly was the BAC increasing after 9 minutes? (mg/mL)/min

(b) How rapidly was it decreasing half an hour later (t = 30)? (mg/mL)/min

1.04 moles of vitamin A2 contain the same number of atoms as 1.000 mol vitamin A

Explanation:

Step 1: Data given

Vitamin A = C20H30O

Vitamin A2 = C20H28O

Step 2: Determine the atoms in vitamin A

Vitamin A has 20 C atoms and 30 H atoms and 1 O-atom

In total we have 51 atoms in vitamin A

Step 3: Calculate numbers of atom in 1 mol

1 mol contains 6.022 * 10^23

For 51 atoms = 51 * 6.022*10^23 = 306 *10^23

Step 4: Determine atoms in vitamin A2

Vitamin A2 has 20 C atoms and 28 H atoms and 1 O-atom

In total we have 49 atoms in vitamin A2

Step 5: Calculate molecules A2

Molecules A2 = 306 *10^23  / 49

molecules A2 = 6.24*10^23

Step 6: Calculate how many moles of vitamin A2 contain the same number of atoms as 1.000 mol vitamin A.

n = 6.24*10^23 / 6.022*10^23 = 1.04 mol

1.04 moles of vitamin A2 contain the same number of atoms as 1.000 mol vitamin A