Chapter 3.1, Problem 26E

Reminder Round all answers two decimals places unless otherwise indicated.

The Sonora Pass California State Highway $108$ crosses the Sierra Nevada mountain range at Sonora Pass, the second highest highway pass ${}^3$ in the Sierra range. The route features striking natural beauty as well as some very steep highway grades. Just west of the pass, one encounters a sign that says “ $28\%$ grade next two miles.” Of course, this means that the maximum grade over the next two miles is $28\%;$ nonetheless, this is an extraordinarily steep state highway. Suppose that the highway is in fact a straight line with a slope of $0.28$ and that the elevation at the beginning is $6000$ feet. What would be the elevation after $2$ horizontal miles? (One mile is $5280$ feet.)