Question

A hot air balloon is sitting on the ground. Hot air was added causing the balloonto ascend at a rate of 4 feet per second for 60 seconds.A. Use integers to write an expression to determine the location of the airballoon relative to its starting location.

Answer 1

Since the rate in which the balloon ascends is constant this means that we can represent its altitude (the location relative to its starting point) as a linear function.

A linear funtion is given by:

$y=mx+b$

where m is the slope or rate of change and b is the y-intecept (the value of y when x=0).

In our case let x be the time it passes since the balloon started ascending and let y be its altitude. With this definition for the variables we conclude that in our case the rate of change is 4 and, since the ballon started on the ground, the valur of b is zero. Therefore the expression we need is:

$y=4x$

Note:

It is important to notice that this expression is only valid for:

$0\leq x\leq60$

This comes from the fact that that the balloon ascends at that rate for 60 seconds and the fact that the time can't be negative.