Chapter 8.4, Problem 4CYU

To determine

To compare:the rates of change for the balloons from 3 to 5 seconds.

Answer to Problem 4CYU

The speed of balloon 1 is more than the speed of balloon 2.

Explanation of Solution

Given:

  

Calculation:

Consider the table that shows relationship between time and altitude of:

Time (s) [x]	Altitude (ft) [y]
	Balloon 1 Balloon 2
3	22.7 30.4
4	30.9 36.0
5	39.1 41.6

The rate of change is change in one quality with respect to another quantity.

Mathematically,

  $Rateof\text{}\text{}\text{}\text{}change=\frac{change\text{}\text{}iny}{changeinx}$

Thus, the rate of change is change in altitude with respect to change in time.

So, the rate of change for the balloon 1 is :

  $\begin{array}{l}\text{Rate of change=}\frac{\text{30}\text{.9-22}\text{.7}}{\text{4-3}}\\ =\frac{8.2}{1}=8.2\end{array}$

So, the rate of change for the balloon 2 is :

  $\begin{array}{l}\text{Rate of change=}\frac{\text{36}\text{.0-30}\text{.4}}{\text{4-3}}\\ =\frac{5.6}{1}=5.6\end{array}$

It means that the speed of balloon 1 is more than the speed of balloon 2.

Conclusion:

Therefore, rate of change for balloon 1 is increase of 8.2 ft/s and balloon 2 is increase of 5.6 ft/s.

It means that the speed of balloon 1 is more than the speed of balloon 2.