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

y = 10^{1.82411-0.0125995x+0.00013401x2}

for awake infants and

y = 10^{1.72858-0.0139928x+0.00017646x2}

for sleeping infants, where x is the age in months.

(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?