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Respiratory Rate Researchers have found that the 95th
Chapter , Problem 112A(choose chapter or problem)
Problem 112A
Respiratory Rate Researchers have found that the 95th percentile (the value at which 95% of the data is at or below) for respiratory rates (in breaths per minute) during the first 3 years of infancy are given by
for awake infants and
for sleeping infants, where x is the age in months. Source: Pediatrics.
a. What is the domain for each function?
b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life?(Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex?)
c. Verify your answer to part b using a graphing calculator.
d. For a 1-year-old infant in the 95th percentile, how much higher is the waking respiratory rate than the sleeping respiratory rate?
Questions & Answers
QUESTION:
Problem 112A
Respiratory Rate Researchers have found that the 95th percentile (the value at which 95% of the data is at or below) for respiratory rates (in breaths per minute) during the first 3 years of infancy are given by
for awake infants and
for sleeping infants, where x is the age in months. Source: Pediatrics.
a. What is the domain for each function?
b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life?(Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex?)
c. Verify your answer to part b using a graphing calculator.
d. For a 1-year-old infant in the 95th percentile, how much higher is the waking respiratory rate than the sleeping respiratory rate?
ANSWER:
Solution :
Step 1 :
In this problem, we have to find the domain of functions and vertex then sketch the graph of the function .