The Gateway Arch in St. Louis, Missouri, is approximately 630 ft wide and 630 ft high. At first glance, the arch resembles a parabola, but its shape is actually known as a modified catenary. The height s (in feet) of the arch, measured from the ground to the middle of the arch, is approximated by the function

where x = 0 represents the center of the arch with –299.2 ≤ x ≤ 299.2.

a. What is the height of the arch when x = 0?

b. What is the slope of the line tangent to the curve when x = 0? Does this make sense?

c. Find the rate of change of the height of the arc when x = 150 ft.

Transcribed Image Text:

s(x) = 693.9 34.38(e0.01003x + e -0.01003x),