Plz help hurry A child's growth and prosperity linear functions worksheet.

Step 1: Rate of Change, slope, and writing linear functions

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

a) Use the data in the table to find the rate of change in the length of the baby girl Grace.

b) Write a linear equation for the graph in point-slope form. Show your work

c) 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 and rate of change.

d) 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.

Step 2: Comparing linear functions

The growth of baby girl Claire is displayed in the graph below

a) Determine the slope of the line. Show your work.

b) Is baby girl Claire growing at a faster rate that the baby girl Grace? Justify your answer.

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

d) Based on the data how long was Claire at birth? Explain.

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.

Function 1: Annual growth of baby girl Grace’s college fund

Y=1,000x + 7,600

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.

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

Step 4: Identifying functions as linear or nonlinear

As infants grow from a toddler to a young adult, there may be time when they are ill and medication is needed. It is extremely important that medication be administered I the exact dose so the child receives the correct amount. To little or too much medication could have serious side effects. A popular children’s fever medicine manufacturer recommends the following dosage information to parents and pediatricians.

Children’s fever medicine
( given every 4-6 hours, as needed)

WEIGHT: (24 lb) (36 lb) (48 lb) (60 lb) (72 lb).

DOSAGE: (5 mL) (7.5 mL) (10 mL) (12.5 mL) (15 mL)

a) Evaluate the dats and find the rate of change from one age group to the next. Explain how you found the rate of change

b) Is the relationship between weight and the amount of medicine linear? Explain.