Question in description

Question

A hot air balloon has already risen 20 feet above the ground. At this point in time it begins to rise at a steady rate of 2 feet per second.

a) What type of function would be a good model for this situation?

b) Sketch a graph representing the balloon’s altitude y in terms of the time x since it resumed its ascent.

c) Identify the intervals on which the graph is increasing or decreasing and explain what these intervals mean in the context of the situation.

Answer 1

(a) Because the hot air balloon is rising at a constant, or steady rate, of 2 ft/sec, this would be an example of a linear function. The 2ft/sec is the slope, meaning the balloon rises 2 feet every 1 second.

(b) Since the hot air balloon has already risen 20 feet, this is the y-intercept (or starting value). The rate is 2 ft/sec. So using slope-intercept form (y = mx + b), the equation is y = 2x + 20. Can you graph this on graph paper, graphing calculator, or Desmos?

(c) The graph is increasing at a steady rate of 2 ft/sec, until the hot air balloon comes back down again. So the graph is increasing from 0 seconds to some time before the hot air balloon descends. From the time the hot air balloon descends, the graph will then be decreasing, meaning the hot air balloon is going donw.

I hope this helps!