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In Example 5, we modeled a measles pathogenesis curve by a function f. A patient infected with the measles virus who has some immunity to the virus has a pathogenesis curve that can be modeled by, for instance, g(t) = 0.9f(t).
(a) If the same threshold concentration of the virus is required for infectiousness to begin as in Example 5, on what day does this occur?
(b) Let P3 be the point on the graph of g where infectiousness begins. It has been shown that infectiousness ends at a point P4 on the graph of g where the line through P3, P4 has the same slope as the line through P1, P2 in Example 5(b). On what day does infectiousness end?
(c) Compute the level of infectiousness for this patient.
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Chapter 6 Solutions
Bundle: Single Variable Calculus: Early Transcendentals, Loose-leaf Version, 8th + Webassign Printed Access Card For Calculus, Multi-term Courses, Life Of Edition
- 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.arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forward
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