Question

A hot air balloon is tethered to the ground by rope that is 200 feet long. The balloon floats into the sky at a rate of 4 feet per second. The equation y=4x gives the height, y, of the balloon x seconds after leaving the ground.

Graph the function
What’s the domain?
What’s the range?
Interpret the x and y intercepts.

Answer 1

Explanation:

y is the height of the balloon. x is the time in seconds.

The balloon starts on the ground, so the smallest value of y is 0. We know the rope is 200 feet long, so the biggest value of y is 200. So the range is 0 ≤ y ≤ 200.

Find the value of x at each end of the range.

When y = 0:

0 = 4x

x = 0

When y = 200:

200 = 4x

x = 50

So the domain is 0 ≤ x ≤ 50.

The x and y-intercept is (0, 0). This means the balloon is initially on the ground.

Graph: desmos.com/calculator/eaavtvbuxm