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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
An egg of a particular bird is nearly spherical. If the radius to the inside of the shell is 5 millimeters and the radius to the outside of the shell is 5.3 millimeters, approximately what is the volume of the shell? [Remember that V = 4/3πr3.]
One hour after x milligrams of a particular drug are given to a person, the change in body temperature T (in degrees Fahrenheit) is given byApproximate the changes in body temperature produced by the following changes in drug dosages: (A) From 2 to 2.1 milligrams (B) From 3 to 3.1 milligrams (C)
If a person learns y items in x hours, as given approximately by y = 52 √x 0 ≤ x ≤ 9 what is the approximate increase in the number of items learned when x changes from 1 to 1.1 hours? From 4 to 4.1 hours?
In Problem, find dy for each function. y = 200x - x2/30
The total cost (in dollars) of producing x electric guitars isC(x) = 1,000 + l00x - 0.25x2(A) Find the exact cost of producing the 51st guitar.(B) Use marginal cost to approximate the cost of producing the 51st guitar.
The total cost (in dollars) of printing x dictionaries is C(x) = 20,000 + 10x (A) Find the average cost per unit if 1,000 dictionaries are produced. (B) Find the marginal average cost at a production level of 1,000 units and interpret the results. (C) Use the results from parts (A) and (B) to
The total profit (in dollars) from the sale of x calendars is P(x) = 22x - 0.2x2- 400 0 ≤ x ≤ 100 (A) Find the exact profit from the sale of the 41st calendar. (B) Use the marginal profit to approximate the profit from the sale of the 41st calendar.
The total profit (in dollars) from the sale of x cameras is P(x) = 12x - 0.02x2 - 1,000 0 ≤ x ≤ 600 Evaluate the marginal profit at the given values of x, and interpret the results. (A) x = 200 (B) x = 350
The total profit (in dollars) from the sale of x gas grills isP(x) = 20x - 0.02x2 - 320 0 ≤ x ≤ 1,000(A) Find the average profit per grill if 40 grills are produced.(B) Find the marginal average profit at a production level of 40 grills and interpret the results.(C) Use the results from
The price p (in dollars) and the demand x for a particular steam iron are related by the equation x = 1,000 - 20p (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x steam irons. What is the domain of R? (C) Find the
The price-demand equation and the cost function for the production of HDTVs are given, respectively, byx = 9,000 - 30p and C(x) = 150,000 + 30xwhere x is the number of HDTVs that can be sold at a price of %p per TV and C(x) is the total cost (in dollars) of producing x TVs.(A) Express the
The company in Problem 39 is also planning to manufacture and market a four-slice toaster. For this toaster, the research department's estimates are a weekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department's
The total cost and the total revenue (in dollars) for the production and sale of x hair dryers are given, respectively, byC(x) = 5x + 2,340 and R(x) = 40x - O.lx2 0 ≤ x ≤ 400(A) Find the value of x where the graph of R(x) has a horizontal tangent line.(B) Find the profit function P(x).(C)
The price-demand equation and the cost function for the production of hand woven silk scarves are given, respectively, byp=60 - 2√xand C(x) = 3,000 + 5xwhere x is the number of scarves that can be sold at a price of $p per unit and C(x) is the total cost (in dollars) of producing x
Table 3 contains price-demand and total cost data for the production of treadmills, where p is the wholesale price (in dollars) of a treadmill for an annual demand of x treadmills and C is the total cost (in dollars) of producing x treadmills.(A) Find a linear regression equation for the
In problem, solve for t or r to two decimal places. 3 = e10r
Use a calculator and a table of values to investigateDo you think this limit exists? If so, what do you think it is ?
It can be shown thatfor any real number s. illustrate this equation graphically for s = 2 by graphing y1 = (1 + 2/n)n y2 = 7.389 056 099 ‰ˆ e2 in the same viewing window, for 1 ‰¤ n ‰¤ 50.
Provident Bank also offers a 3-year CD that earns 3.64% compounded continuously. (A) If $10,000 is invested in this CD, how much will it be worth in 3 years? (B) How long will it take for the account to be worth $11,000?
Use a calculator to evaluate A to the nearest cent in Problem. A = $5,000e0.08t for t = 1,4, and 10
A note will pay $50,000 at maturity 5 years from now. How much should you be willing to pay for the-note now if money is worth 6.4% compounded continuously?
A family paid $99,000 cash for a house. Fifteen years later, the house was sold for $195,000. If interest is compounded continuously, what annual nominal rate of interest did the original $99,000 investment earn?
Referring to Problem 23, in how many years will the $10,000 be due in order for its present value to be $5,000? Problem 23 Solving A = Pert for P, we obtain P = Ae-rt which is the present value of the amount A due in t years if money earns interest at an annual nominal rate r compounded
How long will it take money to double if it is invested at 5% compounded continuously?
At what nominal rate compounded continuously must money be invested to double in 10 years?
A woman invests $5,000 in an account that earns 8.8% compounded continuously and $7,000 in an account that earns 9.6% compounded annually. Use graphical approximation methods to determine how long it will take for her total investment in the two accounts to grow to $20,000.
(A) Show that the rate r that doubles an investment at continuously compounded interest in t years is given by(B) Graph the doubling-rate equation from part (A) for 1 ‰¤ t ‰¤ 20. Is this restriction on t reasonable? Explain.(C) Determine the doubling rates for t = 2,4,6,8,10, and 12 years.
The continuous compound rate of decay of carbon-14 per year is r = -0.000 123 8. How long will it take a certain amount of carbon-14 to decay to half the original amount? Use the radioactive decay model in Problem 33. Radioactive decay model Q = Q0ert where Q0 = amount of the substance at time t =
A strontium isotope has a half-life of 90 years. What is the continuous compound rate of decay? Use the radioactive decay model in Problem 33. Radioactive decay model Q = Q0ert where Q0 = amount of the substance at time t = 0 r = continuous compound rate of decay t = time in years Q = amount of
How long will it take for the U.S. population to double if it continues to grow at a rate of 0.975% per year?
If $4,000 is invested at 8% compounded continuously, graph the amount in the account as a function of time for a period of 6 years.
Some developed nations have population doubling times of 200 years. At what continuous compound rate is the population growing? (Use the population growth model in Problem 37.) Growth Model From Problem 37 P = P0ert Where P0 = population at time t = 0 r = continuous compound rate of growth t =
In Problem, solve for t or r to two decimal places. 2 = e0.03t
In Problem, solve for t or r to two decimal places. 3 = e0.25t
In problem, find fʹ (x). f(x) = ln x8
In problem, find fʹ (x). f(x) = 4 + ln x9
In problem, find fʹ (x). f(x) = ln x10 + 2 ln x
In problem, find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 2 ln x; x = 1
In problem, find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = ex + 1 ; x = 0
In problem, find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 1 + ln x4 ; x = e
In problem, find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 5ex ; = 1
Refer to Problem 23. Does the line tangent to the graph of f(x) = ex at x = 1 pass through the origin? Are there any other lines tangent to the graph of f that pass through the origin? Explain.Problem 23A student claims that the line tangent to the graph of f(x) = ex at x = 3 passes through the
Refer to Problem 25. Does the line tangent to the graph of f(x)=In x at x = e pass through the origin? Are there any other lines tangent to the graph of f that pass through the origin? Explain.Problem 25A student claims that the line tangent to the graph of g(x)=In x at x=3 passes through the
In Problem, first use appropriate properties of logarithms to rewrite f(x), and then find fʹ(x). f(x) = 2 + 3 ln 1/x
In Problem, first use appropriate properties of logarithms to rewrite f(x), and then find fʹ(x). f(x) = x + 5 ln 6x
In Problem, find dy/dx for the indicated function y. y = 4x
In Problem, find dy/dx for the indicated function y. y = log x + 4x2 + 1
In problem, find fʹ (x). f(x) = 6 ln x - x3 + 2
In Problem, find dy/dx for the indicated function y. y = -log2 x + 10 ln x
Use the result of Problem 49 and the four - step process to show that if f (x) = ecx, then f ʹ(x) = cecxProblem 49Explain why
The estimated resale value R (in dollars) of a company car after t years is given by R(t)=20,000(0.86)t What is the rate of depreciation (in dollars per year) after 1 year? 2 years? 3 years?
Repeat Problem 53 for a starting colony of 1,000 bacteria such that a single bacterium divides every 0.25 hour. Problem 53 A single cholera bacterium divides every 0.5 hour to produce two complete cholera bacteria. If we start with a colony of 5,000 bacteria, then after t hours, there will
Refer to Problem 55. Find the weight (to the nearest pound) at which the rate of change of blood pressure with respect to weight is 0.3 millimeter of mercury per pound. Problem 55 An experiment was set up to find a relationship between weight and systolic blood pressure in children. Using hospital
A mathematical model for the average of a group of people learning to type is given by N(t)=10 + 6lnt t ≥ 1 where N(t) is the number of words per minute typed after t hours of instruction and practice (2 hours per day, 5 days per week). What is the rate of learning after 10 hours of instruction
In problem, find fʹ (x). f(x) = ln x + 2ex - 3x2
In problem find fʹ (x) and simplify. f(x) = x2ex
In problem find fʹ (x) and simplify. f(x) = 5x ln x
In problem find fʹ (x) and simplify. f(x) = (3x + 5)(x2 - 3)
In problem find fʹ (x) and simplify. f(x) = (0.5x - 4)(0.2x + 1)
In problem, find fʹ (x) and simplify.
In Problem find fʹ (x) and simplify. f(x) = 5x2(x3 + 2)
In problem, find fʹ (x) and simplify. f(x) = (x2 - 4)(x2 + 5)
In problem, find fʹ (x) and simplify.
In problem, find fʹ (x) and simplify.
In problem, find fʹ (x) and simplify.
In Problem, find hʹ(x), where f (x) is an unspecified differentiable function.
In Problem, find hʹ(x), where f (x) is an unspecified differentiable function.
In Problem find fʹ (x) and simplify. f(x) = (3x + 2)(4x - 5)
In problem, find the indicated derivatives and simplify. yʹ for y = (x3 + 2x2)(3x - 1)
In problem, find the indicated derivatives and simplify.
In problem, find the indicated derivatives and simplify.
In problem, find the indicated derivatives and simplify.
In problem, find the indicated derivatives and simplify.
In problem, find fʹ(x) and find the equation of the line tangent to the graph of f at x =2. f(x) = (7 - 3x)(1 + 2x)
In Problem, find fʹ(x) and find the equation of the line tangent to the graph of f at x =2.
In Problem, find fʹ(x) and find the equation of the line tangent to the graph of f at x =2. f(x) = (x - 2)ln x
In problem find fʹ (x) and find the value of x where fʹ (x) =0 f(x) = (2x - 3)(x2 - 6)
In problem find fʹ (x) and find the value of x where fʹ (x) =0
In Problem find fʹ (x) and simplify.
In Problem, find fʹ(x) in two ways: (1) using the product or quotient rule and (2) simplifying first. f(x) = x4(x3 - 1)
In Problem, find fʹ(x) in two ways: (1) using the product or quotient rule and (2) simplifying first.
In Problem, find each indicated derivative and simplify.
In Problem, find each indicated derivative and simplify.
In Problem, find each indicated derivative and simplify
In Problem, find each indicated derivative and simplify
In Problem, find each indicated derivative and simplify
In Problem, find each indicated derivative and simplify
In Problem, find each indicated derivative and simplify
In Problem, find each indicated derivative and simplify.
In Problem find fʹ (x) and simplify.
In Problem, find each indicated derivative and simplify.
In Problem, find each indicated derivative and simplify.
A communications company has installed a new cable television system in a city. The total number N (in thousands) of subscribers t months after the installation of the system is given by N(t) = 180t/t+ 4 (A) Find (B) Find N(16) and AT(16). Write a brief interpretation of these results. (C) Use the
According to economic theory, the supply A: of a quantity in a free market increases as the price p increases (see the figure).Suppose that the number x of DVD players a retail chain is willing to sell per week at a price of $p is given by (A) Find dx/dp. (B) Find the supply and the instantaneous
One hour after a dose of x milligrams of a particular drug is administered to a person, the change in body temperature T(x),in degrees Fahrenheit, is given approximately byThe rate T'(x) at which T changes with respect to the size of the dosage x is called the sensitivity of the body to the
In Problem, find fʹ (x) and simplify. f(x) = (x - 6)3
In Problem, find fʹ (x) and simplify. f(x) = (3x - 7)5
In Problem, find fʹ (x) and simplify. f(x) = (9 - 5x)2
In Problem, find fʹ (x) and simplify. f(x) = (6 - 0.5x)4
In Problem, find fʹ(x) and simplify. f(x) = (5x2 - 3)6
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