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 a) Use the data in the table to find the rate of change in the length of baby girl Grace. (2 points) b) Write a linear equation for the graph in point-slope form. Show your work. (2 points) 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 of rate of change. (3 points) 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. (2 points)
PLEASE WRITE THE QUESTIONS THEN THE ANSWER PLEAST I WILL NAKE AS BRAILIST PLEASE HELP ME
Answers
a) Rate of change in length = 75%
b) Linear equation of graph formed = 3x - 4y +68 = 0
c) Length of Grace at birth = 17 inches
d) Length of Grace at 36 months = 44 inches
Given,
Age in months
Length in inches
To Find,
a) Rate of change in length
b) Linear equation of graph formed
c) Length of Grace at birth
d) Length of Grace at 36 months
Solution,
Let ‘x’ depict age in months and ‘y’ depict length in inches.
a) If we notice carefully, the gap between two consecutive ages is 2 months and the gap between two lengths is 1.5 inches.
Rate of change of length = Δl/Δt x 100
Δl represents the change in length
Δt represents gap between 2 consecutive age readings
Rate of change of length = 1.5/2 x 100
Rate of change of length = 75%
b) Equation → y = mx + c
Slope = m = Δy/Δx
Δy represents gap between 2 consecutive length readings
Δx represents gap between 2 consecutive age readings
m = 1.5/2 = 3/4
y = (3/4)x + c
4y = 3x + c
At 4 months, her length was 20 inches
Using this, we can find the value of c
4*20 = 3*4 + c
c = 68
Equation → 3x – 4y + 68 = 0
c) Using this equation, we can find the length of Grace at her birth
At birth, x = 0
3*0 – 4y + 68 = 0
4y = 68
y = 17 inches
Thus, her length at birth was 17 inches.
d) Using this equation, we can find the length of Grace at 36 months
x = 36
3*36 – 4y + 68 = 0
4y = 68 + 108
4y = 176
y = 44 inches
Thus, her length at 36 months would be 44 inches.
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Answer:
Step-by-step explanation:
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)