Question

1. -/3 points

the following table shows average lengths of fetuses for selected stages of prenatal development in humans.
month of pregnancy 2 4 6 8
length, in inches 1 7 12 16
(a) what is the average rate of change per month in the length of a fetus from the fourth month of pregnancy to the sixth month of pregnancy?
______ in. per month
(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.
______ in. per month
is this greater than or less than the average rate of change per month from the fourth month to the sixth month?
greater than
less than
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Explanation:

Step1: Recall the formula for average rate of change

The formula for average rate of change is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points.

Step2: Solve part (a)

For part (a), $x_1 = 4$, $y_1=7$, $x_2 = 6$, $y_2 = 12$.
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{12 - 7}{6 - 4}=\frac{5}{2}=2.5$

Step3: Solve part (b)

For part (b), $x_1 = 2$, $y_1 = 1$, $x_2=4$, $y_2 = 7$.
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 1}{4 - 2}=\frac{6}{2}=3$

Answer:

(a) $2.5$ in. per month
(b) $3$ in. per month; greater than