a. To graph: The graph of the weight gain and loss during pregnancy and the 20 weeks following the birth of the baby by assuming that the pregnancy lasts 40 weeks and the delivery occurs immediately after this interval. Solution: The graph of the weight gain and loss during pregnancy is as follows: Explanation: Given information: A women’s weight naturally increases during pregnancy. When she delivers, her weight decreases immediately by the weight of the child. Suppose a 120 lb woman gains 27 lb during pregnancy, delivers a 7 lb baby, and then, through diet and exercise, loses the remaining weight during the next 20 weeks. The weight gain or loss before and after birth is linear. Formula used: (1) Equation of the line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is y − y 1 x − x 1 = y 2 − y 1 x 2 − x 1 Calculation: Here, the vertical axis represents the weight and the horizontal axis represents the time period. At time t = 0 , that is, at the start of pregnancy, weight is 120 lb , which increased after 40 weeks by 27 lb , so at t = 40 , weight is 120 + 27 = 147 lb . Immediately after delivery, that is, after 40 weeks, the weight of the woman decreases by 7 lb , so at t = 40.1 , weight is 140 lb , and remaining weight loss occurs during the next 20 weeks, so at 40 + 20 = 60 weeks, weight is 120 lb . So, coordinates are ( 0 , 120 ) , ( 40 , 147 ) , ( 40.1 , 140 ) , and ( 60 , 120 ) . Now to find the slope of the line passing through the coordinates ( 0 , 120 ) and ( 40 , 147 ) . By using formula for the equation of the line passing through two points, it gives w − 120 t − 0 = 147 − 120 40 − 0 By simplifying, ⇒ w − 120 t = 27 40 By multiplying by t on both sides, ⇒ w − 120 = 27 40 t By adding 120 on both sides, ⇒ w = 27 40 t + 120 Thus, the equation of line is w = 27 40 t + 120 for 0 ≤ t ≤ 40 . Now find the equation of the line passing through coordinates ( 40.1 , 140 ) and ( 60 , 120 ) . By using the formula for the equation of a line passing through two points, it gives w − 120 t − 60 = 140 − 120 40.1 − 60 By simplifying, ⇒ w − 120 t − 60 = 20 − 19.9 By multiplying by t − 60 on both sides, ⇒ w − 120 = − 20 19.9 ( t − 60 ) ⇒ w − 120 = − 20 19.9 t + 1200 19.9 By adding 120 on both sides, ⇒ w = − 20 19.9 t + 1200 19.9 + 120 ⇒ w = − 20 19.9 t + 1200 + 2388 19.9 ⇒ w = − 20 19.9 t + 3588 19.9 Thus, the equation of the line is w = − 20 19.9 t + 3588 19.9 for 40 < t ≤ 60 Thus, we get the function for weight gain and loss during pregnancy and the 20 weeks following the birth of the baby as w = { 27 40 t + 120 , 0 ≤ t ≤ 40 − 20 19.9 t + 3588 19.9 , 40 < t ≤ 60 Therefore, the graph of the weight gain and loss during pregnancy and the 20 weeks following the birth of the baby is as follows:

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Question

Chapter 3.2, Problem 38E

To determine

a.

To graph:

The graph of the weight gain and loss during pregnancy and the 20 weeks following the birth of the baby by assuming that the pregnancy lasts 40 weeks and the delivery occurs immediately after this interval.

Solution:

The graph of the weight gain and loss during pregnancy is as follows:

Explanation:

Given information:

A women’s weight naturally increases during pregnancy. When she delivers, her weight decreases immediately by the weight of the child. Suppose a 120 lb woman gains 27 lb during pregnancy, delivers a 7 lb baby, and then, through diet and exercise, loses the remaining weight during the next 20 weeks. The weight gain or loss before and after birth is linear.

Formula used:

(1) Equation of the line passing through two points (x1, y1) and (x2, y2) is y−y1x−x1=y2−y1x2−x1

Calculation:

Here, the vertical axis represents the weight and the horizontal axis represents the time period.

At time t=0, that is, at the start of pregnancy, weight is 120 lb, which increased after 40 weeks by 27 lb, so at t=40, weight is 120+27=147 lb. Immediately after delivery, that is, after 40 weeks, the weight of the woman decreases by 7 lb, so at t=40.1, weight is 140 lb, and remaining weight loss occurs during the next 20 weeks, so at 40+20=60 weeks, weight is 120 lb.

So, coordinates are (0, 120), (40, 147), (40.1, 140), and (60, 120).

Now to find the slope of the line passing through the coordinates (0, 120) and (40, 147).

By using formula for the equation of the line passing through two points, it gives

w−120t−0=147−12040−0

By simplifying,

⇒w−120t=2740

By multiplying by t on both sides,

⇒w−120=2740t

By adding 120 on both sides,

⇒w=2740t+120

Thus, the equation of line is w=2740t+120 for 0≤t≤40.

Now find the equation of the line passing through coordinates (40.1, 140) and (60, 120).

By using the formula for the equation of a line passing through two points, it gives

w−120t−60=140−12040.1−60

By simplifying,

⇒w−120t−60=20−19.9

By multiplying by t−60 on both sides,

⇒w−120=−2019.9(t−60)

⇒w−120=−2019.9t+120019.9

By adding 120 on both sides,

⇒w=−2019.9t+120019.9+120

⇒w=−2019.9t+1200+238819.9

⇒w=−2019.9t+358819.9

Thus, the equation of the line is w=−2019.9t+358819.9 for 40<t≤60

Thus, we get the function for weight gain and loss during pregnancy and the 20 weeks following the birth of the baby as w={2740t+120,0≤t≤40 −2019.9t+358819.9, 40<t≤60

Therefore, the graph of the weight gain and loss during pregnancy and the 20 weeks following the birth of the baby is as follows:

To determine

b.

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