Problem 1. Let x be the level of precaution, w=16 is the marginal cost of precaution, p(x)=1/x isthe probability of an accident, and A=10,000 is the cost of an accident. Find the efficientprecaution level.

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Answered: Problem 1. Let x be the level of…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter10: Exponential And Logarithmic Functions

Section10.2: Applications Of Exponential Functions

Problem 47PS

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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.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Find the instantaneous rate of change for each function at the given value. f(x)=x2+2x at x=0

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Problem 1. Let x be the level of precaution, w=16 is the marginal cost of precaution, p(x)=1/x is the probability of an accident, and A=10,000 is the cost of an accident. Find the efficient precaution level.