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Mathematical Applications for the Management Life and Social Sciences 11th edition Ronald J. Harshbarger, James J. Reynolds - Solutions

Suppose the presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. The group measures the length across the algae growth
The manufacturer of a medicine wants to test how a new 300-milligram capsule is released into the bloodstream. After a every half-hour, and the number of milligrams of the drug in the bloodstream is calculated. The results obtained are shown in the table.Use 7 rectangles, each with height N (t) at
With U.S. Department of Energy data for selected years from 2000 and projected to 2030, sulphur dioxide emissions from electricity generation (in millions of short tons per year) can be modeled by E(x) = 0.0112x2+0.612x+11.9 Where x is the number of years past 2000 Use n =10 equal subdivisions and
The per capita personal income (in dollars per year) in the United States for selected years from 1960 and projected to 2018 can be modeled by I(t)=13.93t2+136.8t+1971 Where t is the number of years past 1960 (Source: U.S. Bureau of Labor Statistics). Use n=10 equal subdivisions with right-hand
Approximate the area under each curve by evaluating the function at the left-hand endpoints of the subintervals.1. f (x)=4x-x2 from x=0 to x=2; 2 subintervals2. f (x)=x3 from x=0 to x=3; 3 subintervals3. f (x)=9-x2 from x=1 to x=3; 4 subintervals4. f (x)=x2+x+1 from x=-1 to x=1; 4 subintervals
Use the formulas given below to answer the following questions1. Find SL(10) and SR(10).2. Find SL(100) and SR(100).3. Find limn(âˆž SL and limn(âˆž SR.When the area under f (x) = x2 x from x = 0 to x = 2 is approximated, the formulas for the sum of n rectangles using left-hand endpoints and
Evaluate the definite integrals in Problems 1-5.1.2. 3. 4. 5.
Evaluate each integral(a) With the Fundamental Theorem of Calculus and(b) With a graphing calculator (as a check).1.2. 3. 4.
(a) Write the integral that describes the area of the shaded region and(b) Find the area.1.2. 3. 4.
Find the area between the curve y=-x2+3x-2 and the x-axis from x=1 to x=2.
Find the area between the curve y=x2+3x+2 and the x-axis from x=-1 to x=3.
Find the area between the curve y=xex2 and the x-axis from x=1 to x=3.
Find the area between the curve y=e-x and the x-axis from x=-1 to x=1.
In below Problems use the figures to decide which of fa0 f(x) dx or fa0 g(x) dx is larger or if they are equal. Explain your choices.1.2.
In below Problems, use properties of definite integrals. 1. How does f-3-1x√x2+1dx compare with does f-1-3x√x2+1dx 2. If f o-1x3dx=-1/4 and f 10 x3 dx=1/4, what dose f 1-1 x3 dx equal? 3. If f21 (2x-x2) dx = 2/3 and f42 (2x - x2) dx = -20/3, what dose f41 (x2 -2x) dx equal? 4. If f21 (2x-x2)
The rate of depreciation of a building is given by D'(t)=3000(20-t) dollars per year, 0‰¤ t ‰¤ 20; see the figure on the next page.(a) Use the graph to find the total depreciation of the building over the first 10 years (t=0 tot=10).(b) Use a definite integral to find the
The rate of depreciation of a building is given by D'(t)=3000(20-t) dollars per year, ‰¤ t ‰¤20;see the figure below.(a) Use the graph to find the total depreciation of the building over the first 20 years.(b) Use a definite integral to find the total depreciation over the
A store finds that its sales revenue changes at a rate given by S'(t)= - 30t2 + 360t dollars per day Where t is the number of days after an advertising campaign ends and ≤ t ≤ 30 (a) Find the total sales for the first week after the campaign ends (t=0 to t=7). (b) Find the total sales for
The total annual health care costs in the United States (actual and projected, in billions of dollars) for selected years are given in the table. The equation y=4.447x2-9.108x+1055.4 models the annual health care costs, y (in billions of dollars per year), as a function of the umber of years past
The income from an oil change service chain can be considered as flowing continuously at an annual rate given by f (t)=10,000e0.02t (dollars year) Find the total income for this chain over the first 2 years (from t=0 to t=2).
Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by f (t)=120e0.01t in thousands of dollars per year. Find the total income from the machines over the first 3 years.
Using U.S. Energy Information Administration data from 2010 and projected to 2030, the carbon dioxide emissions from biomass energy combustion (in millions of metric tons per year) can be modeled by C(t)=19.12t+319.0 Where t is the number of years past 2010 Evaluate f100C(t)dt and tell what it
The per capita expenditures for U.S. health services and supplies (in dollars per year) for selected years from 2000 and projected to 2018 can be modeled by H (t) =4676e0.053t Where t is the number of years past 2000, evaluate f2010H(t)dt and tell what it represents.
The velocity of blood through a vessel is given by V= K (R2 r2), where K is a constant, R is the (constant) radius of the vessel, and r is the distance of the particular corpuscle from the center of the vessel. The rate of flow can be found by measuring the volume of blood that flows past a point
The rate of production of a new line of products is given by dx/dt =200 [ 1+400/(t+40)2 where x is the number of items produced and t is the number of weeks the products have been in production. 1. How many units were produced in the first 5 weeks? 2. How many units were produced in the sixth week?
The time t (in minutes) needed to read an article appearing on a foreign-language placement test is given by the probability density function f (t)=0.012t2-0.0012t3, ≤ t ≤10 For a test taker chosen at random, find the probability that this person takes 8 minutes or more to read the article.
In a small city the response time t (in minutes) of the fire company is given by the probability density function f(t)=60t2-4t3/16,875, 0≤ t ≤ 15 For a fire chosen at random, find the probability that the response time is 10 minutes or less.
The duration t (in minutes) of customer service calls received by a certain company is given by the probability density function f (t)=0.3e-0.3t, t ≥ 0 Find the probability that a call selected at random lasts (a) 3 minutes or less. (b) Between 5 and 10 minutes.
The useful life of a car battery t (in years) is given by the probability density function f (t)=0.2e-0.2t, t ≥ 0 Find the probability that a battery chosen at random lasts (a) 2 years or less. (b) Between 4 and 6 years.
In the United States, gasoline for motor vehicles is used continuously, and that usage, in billions of gallons per year, is shown in the table for selected years from 2014 and projected to 2024.(a) Find a quadratic function that models these data, with t as the number of years past 2014.Report the
Table 13.1(a) shows the time in seconds that an SRT Viper requires to reach various speeds up to 100 mph. Table 13.1(b) shows the same data, but with speeds in miles per second.(a) Fit a power model to the data in Table 13.1(b).(b) Use a definite integral from 0 to 9.2 of the function you found in
For each shaded region in below Problems,(a) form the integral that represents the area of the shaded region and(b) find the area of the region.1.2. 3. 4. 5.
In below Problems, equations are given whose graphs enclose a region. In each problem, find the area of the region. 1. f (x)=x2+2; g(x)=-x2; x=0; x=2 2. f (x)=x2; g(x)=-1/ 10 (10x); x=0; x=3 3. Y=x3-1; y=x-1; to the right of the y axis 4. y=x2-2x+1; y=x2-5x4; x=2 5. y=1/2 x2; y=x2-2x
In below Problems, find the average value of each function over the given interval.1. f (x)=9-x2 over [0, 3]2. f (x)=2x-x2 over [0, 2]3. f (x)=x3-x over [-1, 1]4. f (x)=1/2 x3+1 over [-2, 0]5. f (x)= √x-2 over [1, 4]
For the product whose total cost and total revenue are shown in the figure, represent total revenue by R(x) and total cost by C(x) and write an integral that gives the average profit for the product over the interval from x0 to x1.
The cost of producing x smart phones is C(x) = x2 + 400x +2000.(a) Use C(x) to find the average cost of producing 1000 smart phones.(b) Find the average value of the cost function C(x) over the interval from 0 to 1000.
The figure shows how an inventory of a product is depleted each quarter of a given year. What is the average inventory per month for the first 3 months for this product? (Assume that the graph is a line joining (0, 1300) and (3, 100).)
The number of daily sales of a product was found to be given by S =100xe-x2 +100 x days after the start of an advertising campaign for this product.(a) Find the average daily sales during the first 20 days of the campaign-that is, from x=0 tox=20.(b) If no new advertising campaign is begun, what is
The demand function for a certain product is given by p= 500 + 1000 / q+1 Where p is the price and q is the number of units demanded. Find the average price as demand ranges from 49 to 99 units.
Suppose that the income from a slot machine in a casino flows continuously at a rate of f (t)=100e0.1t Where t is the time in hours since the casino opened then the total income during the first 10 hours is given by f100 100e0.it dt find the average income over the first 10 hours.
A drug manufacturer has developed a time-release capsule with the number of milligrams of the drug in the bloodstream given by S=30x18/7 - 240x11/ 7+480x4/7 Where x is in hours and 0 ≤ x ≤ 4. Find the average number of milligrams of the drug in the bloodstream for the first 4 hours after a
With data from the U.S. Census Bureau, the Lorenz curves for the income distribution for 2012 in the United States for White non-Hispanic households and for Asian households are given below. Find the Gini coefficient of income for both groups, and compare the distribution of income for these
With U.S. Census Bureau data, the Lorenz curves for the 2012 income distribution in the United States for Black households and for Hispanic households (of any race) are given below. Find the Gini coefficient of income for both groups, and compare the distribution of income for these groups.
In an effort to make the distribution of income more nearly equal, the government of a country asses a tax law that changes the Lorenz curve from y=0.99x2.1 for one year to y=0.32x2+0.68x for the next year. Find the Gini coefficient of income for both years, and compare the distributions of income
The Lorenz curves for the income distribution in the United States for all races for 2012 and for 2004 are given below (Source: U.S. Census Bureau). Find the Gini coefficient of income for both groups, and compare the distribution of income for these groups. 2012: y=x2.760 2004: y=x2.671
Suppose the Gini coefficient of income for a certain country is 2/ 5. Find the value of pif the Lorenz curve for this country is L(x) = 1/3x +2/3 xp
If the Lorenz curve for the income distribution for a given year is L(x)=xp, use integration to find a simple formula for the corresponding Gini coefficient.
If the Lorenz curve for the income distribution for a given year has the form L(x)=xp and the Gini coefficient is G, find a formula for p.
For each shaded region in below Problems,(a) find the points of intersection of the curves,(b) form the integral that represents the area of the shaded region, and(c) find the area of the shaded region.1.2. 3. 4. 5.
Find the total income over the next 10 years from a continuous income stream that has an annual rate of flow at time t given by f (t)=12,000e0.01t (dollars per year).
A continuous income stream has an annual rate of flow at time t given by f (t)=9000e0.12t (dollars per year) Find the present value of this income stream for the next 10 years, if money is worth 6% compounded continuously.
The income from an established chain of Laundromats is a continuous stream with its annual rate of flow at time t given by f (t)=630,000 (dollars per year). If money is worth 7% compounded continuously, find the present value and future value of this chain over the next 5 years.
The profit from an insurance agency can be considered as a continuous income stream with an annual rate of flow at time t given by f (t)=840,000 (dollars per year). Find the present value and future value of this agency over the next 12 years, if money is worth 8% compounded continuously.
Suppose that a printing firm considers its production as a continuous income stream. If the annual rate of flow at time t is given by f (t)=97.5e-0.2(t+3) in thousands of dollars per year, and if money is worth 6% compounded continuously, find the present value and future value of the presses over
Suppose that a vending machine company is considering selling some of its machines. Suppose further that the income from these particular machines is a continuous stream with an annual rate of flow at time t given by f (t)=12e-0.4(t+3) in thousands of dollars per year. Find the present value and
A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Wine Boutique. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by G(t)=30,000 (dollars per year) and the Wine
If the couple in Problem 15 plan to keep the business until age 70 (for the next 12 years), find each present value to see which business is the better buy in this case.
The demand function for a product is p=34-x2. If the equilibrium price is $9 per unit, what is the consumer's surplus? In the following equation p and C are in dollars and x is the number of units.
The demand function for a product is p=100-4x. If the equilibrium price is $40 per unit, what is the consumer's surplus? In the following equation p and C are in dollars and x is the number of units.
The demand function for a product is p=200/ (x+2). If the equilibrium quantity is 8 units, what is the consumer's surplus? In the following equation p and C are in dollars and x is the number of units.
Find the total income over the next 8 years from a continuous income stream with an annual rate of flow at time t given by f (t)=8500e-0.2t (dollars per year).
The demand function for a certain product is p = 100/(1+2x). If the equilibrium quantity is 12 units, what is the consumer's surplus? In the following equation p and C are in dollars and x is the number of units.
The demand function for a certain product is p = 81 - x2 and the supply function is p=x2+4x+11. Find the equilibrium point and the consumer's surplus there. In the following equation p and C are in dollars and x is the number of units.
The demand function for a product is p=49-x2 and the supply function is p=4x+4. Find the equilibrium point and the consumer's surplus there. In the following equation and C are in dollars and x is the number of units.
If the demand function for a product is p=12/ (x+1) and the supply function is p=1+0.2x, find the consumer's surplus under pure competition. In the following equation p and C are in dollars and x is the number of units.
If the demand function for a good is p=110-x2 and the supply function for it is p=2-6/5 X+1/5 x2, find the consumer's surplus under pure competition. In the following equation p and C are in dollars and x is the number of units.
A monopoly has a total cost function C=1000+ 120x+6x2 for its product, which has demand function p=360-3x-2x2. Find the consumer's surplus at the point where the monopoly has maximum profit. In the following equation p and C are in dollars and x is the number of units.
A monopoly has a total cost function C=500+ 2x2+10x for its product, which has demand function p=-1/3x2-2x+30. Find the consumer's surplus at the point where the monopoly has maximum profit. In the following equation p and C are in dollars and x is the number of units.
Suppose that the supply function for a good is p = 4x2 + 2x + 2. If the equilibrium price is $422 per unit, what is the producer's surplus there? In the following equation p is in dollars and x is the number of units.
Suppose that the supply function for a good is p = 0.1x2 = 3x + 20. If the equilibrium price is $36 per unit, what is the producer's surplus there? In the following equation p is in dollars and x is the number of units.
If the supply function for a commodity is p=10ex/3, what is the producer's surplus when 15 units are sold? In the following equation p is in dollars and x is the number of units.
Suppose that a steel company views the production of its continuous caster as a continuous income stream with a monthly rate of flow at time t given by f (t)=24,000e0.03t (dollars per month) Find the total income from this caster in the first year.
If the supply function for a commodity is p=40+ 100 (x+1)2, what is the producer's surplus at x=20? In the following equation p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if its demand function is p=81-x2 and its supply function is p=x2+4x+11. In the following equation p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if its demand function is p=49-x2 and its supply function is p=4x+4. In the following equation p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product with demand function p=12 /(x+1) and supply function p= 1+0.2x. In the following equation p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product with demand function p=110-x2 and supply function p=2-6/5 x+1/5 x2. In the following equation p is in dollars and x is the number of units.
The demand function for a certain product is p=144-2x2 and the supply function is p=x2+33x+48. Find the producer's surplus at the equilibrium point. In the following equation p is in dollars and x is the number of units.
The demand function for a product is p=280-4x-x2 and the supply function for it is P=160+4x+x2. Find the producer's surplus at the equilibrium point. In the following equation p is in dollars and x is the number of units.
Suppose that the Quick-Fix Car Service franchise finds that the income generated by its stores can be modeled by assuming that the income is a continuous stream with a monthly rate of flow at time t given by f (t)=10,000e0.02t (dollars per month) Find the total income from a Quick-Fix store for the
A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by f (t)=80e-0.1t in thousands of dollars per year. Find the income from this stream for the next 10 years.
A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by f (t)=80e-0.1t in thousands of dollars per year. Find the income from this stream for the next 10 years. Discuss.
A franchise models the profit from its store as a continuous income stream with a monthly rate of flow at time t given by f (t)=3000e0.004t (dollars per month) When a new store opens, its manager is judged against the model, with special emphasis on the second half of the first year. Find the
The Medi Spa franchise has a continuous income stream with a monthly rate of flow modeled by f(t)=20,000e0.03t (dollars per month). Find the total income for years 2 through 5.
A continuous income stream has an annual rate of flow at time t given by f (t)=12,000e0.04t (dollars per year) If money is worth 8% compounded continuously, find the present value of this stream for the next 8 years.
Evaluate the integrals in below Problems. Identify the formula used.1.2.3.4.5.
Use formulas or numerical integration with a graphing calculator or computer to evaluate the definite integrals in the following equation1.2.3.4.
If the supply function for x units of a commodity is p=40+100 ln (x+1)2 dollars, what is the producer's surplus at x=20?
If the demand function for wheat is p=/1500 √x2+1 +4 dollars, where x is the number of hundreds of bushels of wheat, what is the consumer's surplus at x=7, p=216.13?
(a) If the marginal cost for x units of a good is MC =√x2+9 (dollars per unit) and if the fixed cost is $300, what is the total cost function of the good? (b)What is the total cost of producing 4 units of this good?
Suppose that the demand function for an appliance is P=400q+400/(q+2)2 where q is the number of units and p is in dollars. What is the consumer's surplus if the equilibrium price is $19 and the equilibrium quantity is 18?
Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow f (t)=10 ln (t+1)-0.1t Where t is time in months and f (t) is in thousands of dollars per month. Find the total income over the next 10 years (120 months).
An isolated community of 1000 people susceptible to a certain disease is exposed when one member returns carrying the disease. If x represents the number infected with the disease at time t (in days), then the rate of change of x is proportional to the product of the number infected, x, and the
use integration by parts to evaluate the integral.1.2.3.4.5.
use integration by parts to evaluate the integral. Note that evaluation may require integration by parts more than once.1.2.3.4.5.
match each of the integrals with the formula or method (I-IV) that should be used to evaluate it. Then evaluate the integral.I Integration by partsII f eu duIII f du/uIV f un du1.2.3.4.5.
If the supply function for x units of a commodity is p=30+50 ln (2x+1)2 dollars, what is the producer's surplus at x=30?
If the marginal cost function for x units of a product is MC=1+3 ln (x+1) dollars per unit and if the fixed cost is $100, find the total cost function.
Suppose that a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by f (t)=10,000-500t (dollars per year) If money is worth 10%, compounded continuously, find the present value of the machine over the next 5 years.
Suppose that the production of a machine used to mine coal is considered as a continuous income stream with annual rate of flow at time t given by f (t)=280,000 - 14,000t (dollars per year) If money is worth 7%, compounded continuously, find the present value of this machine over thse next 8 years.

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