# Math Help - Probability Question Relatiing to Blood Alcohol Level...PLEASE HELP!

1. ## Probability Question Relatiing to Blood Alcohol Level...PLEASE HELP!

hello, I have this math question that i am stuck on..it relates to the blood alcohol level..there is 3 parts to this question.

-The probality (in percent) P of having an automoible accident is related to the blood alcohol content of the driver t by the following function P(t) = e 21.459t

1-The "legal" BAC level in Ohio is .08. If someone was driving at that level, what is the probaliity (in percent) that he or she will be in an accient?

2-At what blood alcohol level would one have to be at in order to have a 50% chance of an accident?

3-At what blood alcohol level would one have to be at in order to have a 75% chance of an accident?

2. I am assuming that this is your equation:

$P(t) = e^{21.459t}$

Is this correct?

3. Yes, that is correct

4. 1) Simply plug in 0.08 into your equation to get your answer:

$
P(0.08) = e^{21.459\cdot 0.08}$

2) Set the expression equal to 50 and solve for t:

$50 = e^{21.459\cdot t}$

Take the natural log of both sides:

$ln 50 = ln e^{21.459\cdot t}$

Using laws of exponents:

$ln 50 = 21.459\cdot t$

Divide both sides by 21.459:

$t = \frac {ln 50}{21.459}$

3) Same as question 2, just with different numbers.