Question

Suppose at the base of a hill a sign reads “Elevation 3500 Feet.” The road goes straight up the hill to the top, which is 3 horizontal miles from the base. At the top, a sign reads “Elevation 4100 Feet.” a) The growth rate in the elevation is ft/mile. (Give your answer as a whole number.) b) The linear relation between the elevation ‘E’, in feet, and horizontal distance ‘h’ , in miles, is E = h + 3500 ; (Give your answer as a whole number.)

Answer 1

The growth rate and linear relationship between Elevation and horizontal distance are :

• Growth rate = 200 ft/mi
• E = 200h + 3500

The growth rate can be calculated thus:

• $\frac{change \: in \: elevation}{change \: in \: horizontal \: distance}$
• Change in elevation = 4100 - 3500 = 600
• Change in horizontal distance = ( 3 - 0) = 3

• Growth rate =
• $\frac{600}{3} = 200 \: feet \: per \: mile$

To linear relationship which exists between elevation and horizontal distance can be written as :

• E = 200h + 3500

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