Answered: 8. DETAILS LARAPCALC10 3.3.062.EP.… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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8.
DETAILS
LARAPCALC10 3.3.062.EP.
Consider the following function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars).
+ 7x2 + 6, 0 < x < 5
6.
R
Find R'(x) and R"(x).
R'(x)
R"(x)
Find the point of diminishing returns for the function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). Use a grap
(x, R) =

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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.
The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
The analysis of tooth shrinkage byC. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yetcome to a halt. In northern Europeans, for example, tooth sizereduction now has a rate of 1% per 1000 years.a. If t represents time in years and y represents tooth size, usethe condition that y = 0.99y0 when t = 1000 to find thevalue of k in the equation y = y0ekt. Then use this value of kto answer the following questions.b. In about how many years will human teeth be 90% of theirpresent size?c. What will be our descendants’ tooth size 20,000 years fromnow (as a percentage of our present tooth size)?
If a company's marginal revenue function is MR(x) = xe−x/9, find the revenue function. [Hint: Evaluate the constant C so that revenue is 0 at x = 0.] R(x)=
suppose that y is an implicit function f(x) defined by the equation x^3 + y^3 = 8xy − 7. find the equation of the normal line to the graph of the inverse f (−1) at the point (2, 1).
A hat manufacturer is planning to expand its workforce. It estimates thatthe number of hats produced by hiring x new workers is given byT(x) = – 0.25 x4 + 6 x3 0 ≤ x ≤ 18a) When is the rate of change of hat production increasing and when is itdecreasing?b) What is the point of diminishing returns (Hint: inflection point) and themaximum rate of change of hat production?
Suppose that a continuous income stream has an annual rate of flow f(t) = 400e−0.03t^2 (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income (in dollars) from this stream over the next 3 years. (Round your answer to the nearest dollar.)

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