Beginning Algebra With Applications, Chapter 5, 5.1, Section 5.1, Problem 32

The following table shows average lengths of fetuses for selected stages of prenatal development in humans.

$\begin{array}{c|cccc} \text{Month of pregnancy} & 2 & 4 & 6 & 8 \\ \hline\\ \text{Length, in inches} & 1 & 7 & 12 & 16 \end{array}$

a. What is the average rate of change per month in the length of a fetus from the sixth month of pregnancy to the eighth month of pregnancy?


$\begin{equation} \begin{aligned} \text{average rate of change} =& \frac{\text{length of a fetus in eighth month - length of fetus in sixth month}}{8-6} \\ \\ =& \frac{16-12}{8-6} \\ \\ =& \frac{4}{2} \\ \\ =& 2 \text{ inches} \end{aligned} \end{equation}$



The average rate of change per month is 2 inches.

b. Find the average rate of change per month in the length of a fetus from the second month of pregnancy to the fourth month of pregnancy. Is this greater than or less than the average rate of change per month from the sixth month to the eighth month?


$\begin{equation} \begin{aligned} \text{average rate of change} =& \frac{\text{length of the fetus in fourth month - length of fetus in second month}}{4-2} \\ \\ =& \frac{7-1}{4-2} \\ \\ =& \frac{6}{2} \\ \\ =& 3 \text{ inches} \end{aligned} \end{equation}$



The average rate of change per month from fourth month of pregnancy to the second month of pregnancy is 3 inches. And it is greater than the average rate if change per month from the sixth month to the eighth month.