## A shop has determined that the number of bottles of water they sell on a summer day is a function of the day’s high temperature, and is approximately given by ?(?) = 4? + 27, where ? is the day’s high temperature, and 80 ≤ ? ≤ 110.

### mathematics

##### Description

1. A shop has determined that the number of bottles of water they sell on a summer day is a function of the day’s high temperature, and is approximately given by ?(?) = 4? + 27, where ? is the day’s high temperature, and 80 ≤ ? ≤ 110. Suppose that the predicted high temperatures for the next 7 days are given in the table below. Express the high temperature as a function of the day. Use this function to create a function that represents the number of bottles of water sold as a function of the day. Pick one ordered pair on the graph of the new function, and explain what it tells you in practical terms.

2. An accident at an oil drilling platform is causing a circular-shaped oil slick to form. The volume of the oil slick is roughly given by ?(?) = 0.08?? 2 , where ? is the radius of the slick in feet. In turn, the radius is increasing over time according to the function ?(?) = 0.5?, where ? is measured in minutes. Find (? ∘ ?)(?), and give a practical interpretation of what this function tells you. After how many minutes will the volume of the slick be 225 cubic feet?

3. The following table shows the number of motor vehicle crash deaths for teens aged 13-19, separated by gender, for the years 2005-2015 (Data source: iihs.org). Create a table for each of these functions: (? + ?)(?) and (? − ?)(?). Describe what each of these two functions tells you in practical terms. Is the function (? + ?)(?) increasing or decreasing? What does this tell you?

4. The following graph shows the average retail price of regular gasoline in Tucson and Albuquerque over the 3 month period. Suppose ?(?) represents the price of gas in Tucson as a function of the day, and ?(?) represents the price of gas in Albuquerque as a function of the day. For which dates is the function (? − ?)(?)positive? Negative? Zero? What do each of these answers tell us about the price of gas in Tucson and Albuquerque? (Data source: gasbuddy.com)