Example 4 You are at the base of a trail on Mount Rainier in Washington. The temperature is 50.9°F. The temperature changes at a rate of 0.005°F per foot.

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Example 4 You are at the base of a trail on Mount Rainier in Washington. The temperature is 50.9°F. The temperature changes at a rate of 0.005°F per foot of elevation as you hike up. What is the temperature 1000 feet above the base? HIKING Writing an Equation SOLUTION STEP 1Write a verbal model to describe the situation. –

Example 4 Writing an Equation STEP 2Write a matching algebraic model in slope- intercept form. Let y be the temperature and x be the increase in elevation. y = bmxmx+ Write slope-intercept form. STEP 3Substitute for m and b. The temperature changes at a rate of 0.005°F per foot, so. The initial temperature is 50.9°F, so b – m = – = y = 0.005x – Substitute for m and 50.9 for b –

Example 4 Writing an Equation STEP 4Find the value of y when x = Write the equation. y = 0.005x – Substitute 1000 for x. = – () Simplify. = 45.9 ANSWER The temperature 1000 feet above the base is 45.9°F.

Guided Practice 10.WHAT IF? In Example 4, suppose the temperature at the base of the trail is 55.2°F. What is the temperature 2500 feet above the base? ANSWER 42.7°F for Example 4 11.CHARITY EVENT You are participating in a walk for charity. One donor will give you $4 for each mile you walk. Another donor gives you $25, a fixed amount that does not depend on how far you walk. How much money will you raise if you walk 6 miles? ANSWER $49