\

If an initial quantity $\"\"$ continuous grows at an exponential rate $\"\"$ , then the final amount $\"\"$ after a time $\"\"$ is given by the following formula $\"\"$ . $\"\"$

\

(a)

\

Find percent chance of having a car accident at this concentration.

\

The function is $\"\"$ , where $\"\"$ is the percent chance of an accident and $\"\"$ is the drivers blood alcohol concentration $\"\"$ .

\

Since the legal BAC is 0.08, $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Percent chance of having a car accident at this concentration is $\"\"$ .

\

$\"\"$

\

(b)

\

Find BAC would correspond to a 50% chance of having a car accident.

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Apply logarithm on each side.

\

$\"\"$

\

$\"\"$ .

\

BAC would correspond to a 50% chance of having a car accident is $\"\"$ .

\

$\"\"$

\

(a) Percent chance of having a car accident at this concentration $\"\"$ .

\

(b) BAC would correspond to a 50% chance of having a car accident is $\"\"$ .