Question

Given: The function f(x) will model the roller coaster's height from the ground in feet over time, measured in seconds since the ride started.

f(x) = 5(2) 0 < x < 4
f(x) = -5x² + 40x 4 f(x) = 35 7 < x < 9
f(x) = -5(x - 12)² + 80 9 < x < 12
f(x) = _____ 12 < x < 15
f(x) = _____ 15 < x < 17
f(x) = 2.5x - 22.5 17 f(x) = -15x + 380 23 < x < 25
f(x) = 5 25 < x < 27


When does the roller coaster reach 100 feet above the ground?

Answer 1

The roller coaster's height above the ground in relation to time is modeled by a piecewise function. To find when it reaches 100 feet, the function's relevant segment is set equal to 100 and solved for time x.

Step-by-step explanation:

To determine when the roller coaster reaches 100 feet above the ground, we need to analyze the given piecewise function for the height of the roller coaster, f(x), with respect to time x in seconds. The function provided has several segments, and we need to find which one corresponds to the roller coaster reaching 100 feet.

The segments provided are generally in the form of linear functions or quadratic functions, which model different parts of the roller coaster's journey. For instance, f(x) = -5x² + 40x is likely to represent the roller coaster ascending or descending with acceleration, as it is a quadratic function.

To find the point at which the roller coaster is 100 feet high, we set the appropriate function equal to 100 and solve for x. For example, if we were to consider the quadratic function mentioned, we would set up the equation -5x² + 40x = 100 and solve for x to find the time at which this height is reached, if at all during this segment.