Exponential Function Project

In 2009, the number of alcohol-related fatalities accounted for 12,744 deaths throughout the United States. During that year, 51% (114/223) of all Connecticut’s fatal automobile accidents involved an intoxicated driver. Because of this, laws against drunk driving are getting tougher and tougher. Not just stiffer penalties, but law enforcement agencies are more active as well. Remember that alcohol impairs your ability to drive sooner than you think!

Resource: Information retrieved from AlcoholAlert.com on 11/6/12

The percent risk, R, of an auto accident can be found by: R = 6e^12.77x where x is the blood alcohol concentration (percent) of the driver.

In many states it is illegal to drive with a blood alcohol concentration of 0.08.

Both variables x and R are percent numbers and should not be converted to a decimal.

For example, an R of 40.74 when x is 0.15 means that a person would have a 40.74% chance of having a driving accident if his or her alcohol blood level was measured at 0.15%

1. What is the percent risk (R) if the blood alcohol concentration is 0.1. Show all work

(Note: Use 0.1 not 0.001 in the calculation and round to the nearest tenth) (3 pts)

1. Double the blood alcohol concentration (use 0.2) used in question #1. Show all work

What is the percent risk now? (round to the nearest tenth). (2 pts)

1. Was the Risk for a 0.2 concentration double that of a 0.1 concentration? Was it more than double or less? Explain. Did the percent risk answer to #3 surprise you? Explain why or why not. (4 pts)

1. At what blood alcohol concentration level, x, of the driver would there be an accident nearly certain to happen? Show all work. (R = 100 then solve for x, go out three decimal places)

Use the graphing mode on your calculator, graph the equation y = 6e^12.77x to represent the percent risk model. (2 pts)

Y= CLEAR out all equations, place cursor after Y1

6 * 2^nd ^ (12.77 *X) Notice e is above the division sign. To get the X, use the variable button (X,T,θ,n button)

WINDOW Window button is in the top graphing section of the calc.

Make the following changes in the window:

Xmin = 0

Xmax=0.29375

Xscl=0.05

Ymin= -15

Ymax=105

Yscl= 25

Xres=1

GRAPH

TRACE

After you hit TRACE on your calculator, move the cursor using the arrow key until

Y = 100. What is the X coordinate? Round to the nearest tenth.

Explain what this point represents. (3 pts)

1. The graph you see on your screen is an increasing exponential function. After you hit TRACE on your calculator, move the cursor using the arrow key until X = 0.08. What is the Y coordinate? Round to the nearest tenth. (3 pts)

1. Interpret the meaning of X and Y relating to the exponential model from page 1 using complete sentences. (2 pts)

1. What is the legal limit for the blood alcohol level percent in Michigan or the state you live in for a DUI conviction for someone 21 or older? You may have to do some research if you are not aware of MI or your state laws. (1 pts)

Given the table below of blood alcohol percents, answer the following using your own approximate weight.

MEN
Drinks	Body Weight in Pounds
	100	120	140	160	180	200	220	240
0	.00	.00	.00	.00	.00	.00	.00	.00
0	.00	.00	.00	.00	.00	.00	.00	.00
1	.04	.03	.03	.02	.02	.02	.02	.02
2	.08	.06	.05	.05	.04	.04	.03	.03
3	.11	.09	.08	.07	.06	.06	.05	.05
4	.15	.12	.11	.09	.08	.08	.07	.06
5	.19	.16	.13	.12	.11	.09	.09	.08
6	.23	.19	.16	.14	.13	.11	.10	.09
7	.26	.22	.19	.16	.15	.13	.12	.11
8	.30	.25	.21	.19	.17	.15	.14	.13
9	.34	.28	.24	.21	.19	.17	.15	.14
10	.38	.31	.27	.23	.21	.19	.17	.16

**Subtract 0.01 for each 40 minutes of drinking**

WOMEN
Drinks	Body Weight in Pounds
	90	100	120	140	160	180	200	220	240
0	.00	.00	.00	.00	.00	.00	.00	.00	.00
0	.00	.00	.00	.00	.00	.00	.00	.00	.00
1	.05	.05	.04	.03	.03	.03	.02	.02	.02
2	.10	.09	.08	.07	.06	.05	.05	.04	.04
3	.15	.14	.11	.10	.09	.08	.07	.06	.06
4	.20	.18	.15	.13	.11	.10	.09	.08	.08
5	.25	.23	.19	.16	.14	.13	.11	.10	.09
6	.30	.27	.23	.19	.17	.15	.14	.12	.11
7	.35	.32	.27	.23	.20	.18	.16	.14	.13
8	.40	.36	.30	.26	.23	.20	.18	.17	.15
9	.45	.41	.34	.29	.26	.23	.20	.19	.17
10	.51	.45	.38	.32	.28	.25	.23	.21	.19

**Subtract 0.01 for each 40 minutes of drinking**

Assume that you have been consuming the number of alcoholic drinks given in the questions below for 2 hours (120 minutes) then answer the following.

1. What is your approximate weight in the table? (1 pts)

1. According to the table what will be your blood alcohol concentration after consuming 2 drinks? Show all work (2 pts)

1. What is your level after subtracting 0.01 for each 40 minutes of drinking (2 pts)

1. Calculate your percent chance of having an accident. Show all work (3 pts)

1. For 5 drinks what will be your blood alcohol percent level (remember to subtract 0.01 for each 40 minutes of drinking)? Show all work (2 pts)

1. Calculate your percent chance of having an accident. Show all work (3 pts)

1. For 8 drinks what will be your blood alcohol percent level (remember to subtract 0.01 for each 40 minutes of drinking)? Show all work (2 pts)

1. Calculate your percent chance of having an accident . Show all work (3 pts)

Discussion: Write a summary of the above findings (1 – 2 paragraphs). Were you surprised by the results? What did you notice about the exponential nature of the risk? What was learned by going through this exercise? (5 pts)