SECTION 2 4 Using Linear Models Example 1

SECTION 2. 4 Using Linear Models

Example 1 � Transportation: Jacksonville, Florida has an elevation of 12 ft above sea level. A hot-air balloon taking off from Jacksonville rises 50 ft/min. Write an equation to model the balloon’s elevation as a function of time. Graph the equation. Interpret the intercept at which the graph intersects the vertical axis.

Example 2 � Hot-air Balloon: Suppose a balloon begins descending at a rate of 20 ft/min from an elevation of 1350 ft. � Write an equation to model the balloon’s elevation as a function of time. What is true about the slope of this line? � Graph the equation. Interpret the intercept.

Example 3 � Science: A candle is 6 in. tall after burning for 1 h. After 3 h. it is 5 ½ in. tall. Write a linear equation to model the height y of the candle after burning x hours. � What does the slope represent? � What does the y-intercept represent? � Another candle is 7 in. tall after burning for 1 h and 5 in. tall after burning for 2 h. Write a linear equation to model the height of the candle.

Example 4 � Example 4: Using a Linear Model: � Use the equation in Example 3. In how many hours will the candle be 4 in. tall? � How tall will the candle be after burning for 11 h? � What was the original height of the candle? � When will the candle burn out?

Example 5 � Automobiles A woman is considering buying a 1999 car priced at $4200. She researches prices for various years of the same model and records the data in a table. Model Year 2000 2001 2002 2003 2004 Prices $5784 $5435 $6810 $6207 $8237 $7751 $9660 $9127 $10, 948 $10, 455 � Let x represent the model year. Let y be the price of the car. Draw a scatter plot. Decide whether a linear model is reasonable. � Draw a trend line. Write an equation of the line. Determine whether the asking price is reasonable.