5.) (10 pts) The following graphs show survival in the U.S. from 1900 (left-most curve) to 2020 (right-most curve) in 10-year intervals. Estimate the median lifespan in (a) 1900 (b) 1940, and (c) 2020. 100 90 Percent Surviving 70 60 50 40 30 10 882882820° 2020 1900 0 228288 28 28 2 2 Age

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=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 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.

What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?