A Child’s Growth and Prosperity When a new baby enters this world, pediatricians will monitor the baby’s growth in many areas. Weight, head circumference, length, and body mass index are just a few of the measurements collected as newborns progress through childhood. Parents of newborns are not only concerned with their child’s measurements, but they typically consider their child’s medical and financial needs, too.

As you complete the task, keep these questions in mind: How can you use linear functions to describe and analyze measurements associated with babies’ growth? How can you use functions to calculate college savings and to determine how much medicine to administer?
Directions:
Complete each of the following tasks, reading the directions carefully as you go.
You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.
Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy.
Now let’s get started!
Step 1: Rate of change, slope, and writing linear functions

Pediatricians will measure and track the growth of an infant’s weight and length to be sure the baby is thriving and growing properly. The growth of baby girl Grace is displayed in the data table below.

Growth Chart for Baby Girl Grace
(4–30 Months)
Months 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Length (inches) 20 21.5 23 24.5 26 27.5 29 30.5 32 33.5 35 36.5 38 39.5

⦁ Use the data in the table to find the rate of change in the length of baby girl Grace. (2 points)

⦁ Write a linear equation for the graph in point-slope form. Show your work. (2 points)

⦁ Use your equation to determine how long Grace was at birth. Show your work and explain how you can check your result using your knowledge of rate of change. (3 points)

⦁ Based on the data, how long do you predict baby Grace will be at 36 months of age? Use the rate of change to justify your answer. Does your answer make sense? Explain. (2 points)

Step 2: Comparing linear functions
The growth of baby girl Claire is displayed in the graph below.

⦁ Determine the slope of the line. Show your work. (2 points)

⦁ Is baby girl Claire growing at a faster rate than baby girl Grace? Justify your answer. (2 points)

⦁ Use point-slope form to write a linear equation to represent the growth of Claire over time. Then, simplify the equation and write it in slope-intercept form. Identify the y-intercept. Show your work. (3 points)

⦁ Based on the data, how long was Claire at birth? Explain. (2 points)

Step 3: Applying linear functions
Grace and Claire’s parents are saving money now for their college education. Function 1 shows the growth of baby Grace’s college fund over time. Function 2 shows growth of baby Claire’s college fund over time.

a) If Grace and Claire’s parents each invested $7,600 into a college saving account when the girls were born, how much money will each girl have for college when she turns 18? Explain. (2 points)

b) Do the functions show a positive or negative correlation between time and the amount of money saved? Explain. (1 point)

Step 4: Identifying functions as linear or nonlinear
As infants grow from a toddler to a young adult, there may be times when they are ill and medication is needed. It is extremely important that medication be administered in the exact dose so the child receives the correct amount. Too little or too much .