General: Airplane Flight Path A plane is to take off and reach a level cruising altitude...

General: Airplane Flight Path A plane is to take off and reach a level cruising altitude of 5 miles after a horizontal distance of 100 miles, as shown in the following diagram. Find a polynomial flight path of the form f(x) = ax³ + bx² + cx + d by following Steps i to iv to determine the constants a, b, c, and d.

i. Use the fact that the plane is on the ground at x = 0 [that is, f(0) = 0] to determine the value of d.

ii. Use the fact that the path is horizontal at x = 0 [that is, to determine the value of c.

iii. Use the fact that at x = 100 the height is 5 and the path is horizontal to determine the values of a and b. State the function f(x) that you have determined.

iv. Use a graphing calculator to graph your function on the window [0, 100] by [0, 6] to verify its shape.