In sixteen states and the District of Columbia, the legal blood-alcohol level is 0.08. Use the formula A(x) = -0.0082x2 + 0.06x to compute blood-alcohol levels as a function of x (the time in hours). When is the first time that a person can be arrested for drunken driving after drinking 5 ounces of 80-proof whiskey in those states? (Hint: To find an answer through approximation, calculate the blood-alcohol level for every 0.2 hours beginning at x = 0.2.)

Question

In sixteen states and the District of Columbia, the legal blood-alcohol level is 0.08. Use the formula A(x) = -0.0082x2 + 0.06x to compute blood-alcohol levels as a function of x (the time in hours). When is the first time that a person can be arrested for drunken driving after drinking 5 ounces of 80-proof whiskey in those states? (Hint: To find an answer through approximation, calculate the blood-alcohol level for every 0.2 hours beginning at x = 0.2.)

1.8 hours
2.2 hours
1.6 hours
3.0 hours

I don't understand the hint - it really made my confusion worse.

Answer 1

To understand the hint provided, let's break down the problem step by step.

First, let's analyze the given formula: A(x) = -0.0082x^2 + 0.06x. This formula represents the blood-alcohol level as a function of time (x) in hours.

The hint suggests approximating the time at which a person can be arrested for drunken driving after consuming 5 ounces of 80-proof whiskey. To do this, we need to calculate the blood-alcohol level at various time intervals, starting from x = 0.2 and increasing by 0.2 at each step.

We can use the given formula to calculate the blood-alcohol level at each time interval. Let's apply this approach:

1. For x = 0.2 hours:
A(0.2) = -0.0082(0.2)^2 + 0.06(0.2)

2. For x = 0.4 hours:
A(0.4) = -0.0082(0.4)^2 + 0.06(0.4)

3. For x = 0.6 hours:
A(0.6) = -0.0082(0.6)^2 + 0.06(0.6)

4. Continue this process until you find the first time (x) at which the blood-alcohol level (A(x)) exceeds or equals 0.08, which is the legal limit.

For example, you may need to calculate A(x) for x = 0.8, 1.0, 1.2, and so on, until you find the value of x that makes A(x) equal to or greater than 0.08.

Keep in mind that the answer choices provided (1.8 hours, 2.2 hours, 1.6 hours, 3.0 hours) are possible results obtained through this method of approximation. The closest approximation among these options would be the correct answer to the question.

I hope this explanation clarifies the hint and helps you understand the process of approximating the time at which a person can be arrested for drunken driving.