Chapter 8.4, Problem 11PPS

To determine

To compare:Rate of change for each linear function.

Answer to Problem 11PPS

The rate of changefor mosquitoes is increase of $\text{600 beats/second}$ and the rate of change for honey bees is increase of $\text{200 beats/second}\text{.}$

Explanation of Solution

Given:

  

Calculation:

Consider the table that shows time and number of beats taken by mosquitoes:

Time (s) [x]	Number of beats [y]
0.5	300
1	600

And also, make the table that shows time and number of beats taken by honey bees:

Time (s) [x]	Number of beats [y]
1	200
2	400

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 number of beats with respect to change in time.

So, the rate of change for mosquitoes is:

Rate of change = $\frac{600-300}{1-0.5}=\frac{300}{0.5}=600$

And, the rate of change for honey bees is:

Rate of change = $\frac{400-200}{2-1}=\frac{200}{1}=200$

The rate of change for mosquitoes is increase of $\text{600 beats/second}$ and the rate of change for honey bees is increase of $\text{200 beats/second}\text{.}$

It means that number of time a mosquito’s wings beats increased at a faster rate than the number of times honey bees wings beats.

Conclusion:

The rate of change for mosquitoes is increase of $\text{600 beats/second}$ and the rate of change for honey bees is increase of $\text{200 beats/second}\text{.}$