The grade of a road is defined as the distance it rises (or falls) to the distance it runs horizontally, usually expressed as a percentage. Consider a road with positive grade, g.
Suppose that you begin driving on that road at an altitude a0.
a. Find the linear equation that expresses the altitude, a, when you have driven a distance, d, along the road. (Hint: Draw a graph and apply the Pythagorean Theorem.)
b. Identify and interpret the y-intercept and slope of the linear equation in part (a).
c. Apply your results in parts (a) and (b) to a road with a 5% grade and an initial altitude of 1 mile. Express your answer for the slope to four decimal places.
d. For the road in part (c), what altitude will you reach after driving 10 miles along the road?
e. For the road in part (c), how far along the road must you drive to reach an altitude of 3 miles?