Chapter 2.CR, Problem 111CR

Respiratory Rate Researchers have found that the $95$ th percentile (the value at which $95\%$ of the data are at or below) for respiratory rates (in breath per minute) during the first $3$ years of infancy are given by

$y={10}^{1.82411-0.0125995x+0.00013401x^2}$

for awake infants and

$y={10}^{1.72858-0.0139928x+0.00017646x^2}$

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 $95$ th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate?

e.

f.