During a hot-­‐air balloon festival, data were gathered on the height y of a balloon after x minutes.

Question

During a hot-air balloon festival, data were gathered on the height (y) of a balloon after (x) minutes. Hot air balloon height

Time(min): 0, 2, 4, 6, 8.

Height(m): 15, 85, 155, 225, 295

A. Is the rate of change constant? If so, what is the rate of change and what does it represent?

B. Write a linear equation in slope-­‐intercept form to model this situation.

C. If the balloon continues to rise at the same rate, use function notation to express the height after 12 minutes. 

D. Provide the domain given that the maximum allowed height is 500 meters.

Answer 1

A) Yes, rate of change = r = 70/2 = 35 m/min

B) Height = h = f(t) = 35t + 15

C) f(12) = 35(12)+15 = 435 m

D) Need to solve for amount of time to reach 500 meters

35t+15=500

t = 485/35 ≈ 13.857 minutes

Domain: [0,13.857]

Answer 2