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college mathematics for business

Questions and Answers of College Mathematics For Business

The number of voters (in thousands) in a certain city is given byN(t) = 20 + 4t - 5te-0.1twhere t is time in years. Find the average number of voters during the period from t = 0 to t = 5.
An oil tanker is producing an oil slick that is radiating outward at a rate given approximately bywhere R is the radius (in feet) of the circular slick after t minutes. Find the radius of the slick
A student enrolled in an advanced typing class progressed at a rate ofN′(t) = (t + 6)e-0.25twords per minute per week t weeks after enrolling in a 15- week course. If a student could type 40 words
The concentration of particulate matter (in parts per million) t hours after a factory ceases operation for the day is given byFind the average concentration for the period from t = 0 to t = 5. 20 In
The marginal profit for a small car agency that sells x cars per week is given bywhere P(x) is the profit in dollars. The agency’s profit on the sale of only 1 car per week is - $2,000. Find the
A yeast culture is growing at a rate of W′(t) = 0.3e0.1t grams per hour. Find the area between the graph of W′ and the t axis over the interval [0, 10] and interpret the results.
The data in the following table describe the distribution of wealth in a country:(A) Use quadratic regression to find the equation of a Lorenz curve for the data.(B) Use the regression equation and a
The following tables give price–demand and price–supply data for the sale of soybeans at a grain market, where x is the number of bushels of soybeans (in thousands of bushels) and p is the price
Lorenz curves also can provide a relative measure of the distribution of a country’s total assets. Using data in a report by the U.S. Congressional Joint Economic Committee, an economist produced
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
After test marketing a new high-fiber cereal, the market research department of a major food producer estimates that monthly sales (in millions of dollars) will grow at the monthly rate oft months
Find the consumers’ surplus (to the nearest dollar) at a price level of P ̅ = $2.089 for the price– demand equationp = D(x) = 9 - ln (x + 4)Use x computed to the nearest higher unit.
In a study on the effects of World War II on the U.S. economy, an economist used data from the U.S. Census Bureau to produce the following Lorenz curves for the distribution of U.S. income in 1935
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
Monthly sales of a particular personal computer are expected to increase at the rate ofS′(t) = -4te0.1tcomputers per month, where t is time in months and S(t) is the number of computers sold each
An amusement company maintains records for each video game it installs in an arcade. Suppose that C(t) and R(t) represent the total accumulated costs and revenues (in thousands of dollars),
Find the Gini index of income concentration for the Lorenz curve with equationUse Table 1 to evaluate all integrals involved in any solutions of Problem. y = rV1 + 3x
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
Using production and geological data, the management of an oil company estimates that oil will be pumped from a producing field at a rate given bywhere R(t) is the rate of production (in thousands of
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
In Problem find the constant c (to two decimal places) such that the Lorenz curve f (x) = xc has the given Gini index of income concentration.0.37
In Problem find the consumers’ surplus and the producers’ surplus at the equilibrium price level for the given price– demand and price–supply equations. Include a graph that identifies the
In Problem set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. 2. y = V9 – x²; y =
Find the Gini index of income concentration for the Lorenz curve with equationy = xex - 1
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
Rats were trained to go through a maze by rewarding them with a food pellet upon successful completion of the run. After the seventh successful run, the probability density function for length of
The rate of flow f(t) of a continuous income stream is a linear function, decreasing from $10,000 per year when t = 0 to $5,000 per year when t = 8. Find the total income produced in the first 8
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. y = -V16 – x; y = 0;
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
The rate of flow f(t) of a continuous income stream is a linear function, decreasing from $12,000 per year when t = 0 to $9,000 per year when t = 10. Find the total income produced in the first 10
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. y = -V4 – x; y = V4
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.y = ex; y = e-x; 0 ≤ x ≤ 4
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.y = ex; y = -e-x; 1 ≤ x ≤ 2
If f(x) = ax2 + bx + c, where a, b, and c are any real numbers, use Simpson’s rule with n = 1 (so there are 2n = 2 subintervals) to show that S2 f(x) dx. ||
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.y = x3 - 3x2 - 9x + 12; y = x + 12
If f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are any real numbers, use Simpson’s rule with n = 1 (so there are 2n = 2 subintervals) to show that S2 f(x) dx. ||
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem find the area bounded by the graphs of the indicated equations over the given interval (when stated). Compute answers to three decimal places.y = x3 - 6x2 + 9x; y = x
In Problem find the area bounded by the graphs of y = f(x) and y = g(x) to two decimal places. Use a graphing calculator to approximate intersection points to two decimal places. f(x) 10 g(x) = x +
In Problem use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.y = x3 + x2 - 2x -
In Problem use absolute value on a graphing calculator to find the area between the curve and the x axis over the given interval. Find answers to two decimal places.y = x5ex; - 2 ≤ x ≤ 2
A business is planning to purchase a piece of equipment that will produce a continuous stream of income for 8 years with rate of flow f(t) = 9,000. If the continuous income stream earns 6.95%,
In Problem find the area bounded by the graphs of y = f(x) and y = g(x) to two decimal places. Use a graphing calculator to approximate intersection points to two decimal places. f(x) = V1 + x²;
In Problem find the area bounded by the graphs of y = f(x) and y = g(x) to two decimal places. Use a graphing calculator to approximate intersection points to two decimal places. f(x) = xV4 + x; g(x)
In Problem use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.y = ex + 1; y = 2
In Problem find the area bounded by the graphs of y = f(x) and y = g(x) to two decimal places. Use a graphing calculator to approximate intersection points to two decimal places. f(x) ;g(x) = x- 2 Vx
In Problem use absolute value on a graphing calculator to find the area between the curve and the x axis over the given interval. Find answers to two decimal places.y = (4 - x) ln x; 1 ≤ x ≤ 7
Find the consumers’ surplus at a price level of p = $150 for the price–demand equationp = D(x) = 400 - 0.05x
In Problem use a graphing calculator to graph the equations and find relevant intersection points. Then find the area bounded by the curves. Compute answers to three decimal places.y = ln x; y = x2 -
Find the consumers’ surplus at a price level of P̅ = $15 for the price–demand equationUse Table 1 to evaluate all integrals involved in any solutions of Problem. 7,500 – 30x p = D(x) %3D 300 -
In Problem use absolute value on a graphing calculator to find the area between the curve and the x axis over the given interval. Find answers to two decimal places.y = (x - 1)ex2; 0 ≤ x ≤ 2
In Problem use absolute value on a graphing calculator to find the area bounded by the graphs of the equations over the given interval. Compute answers to three decimal places.y = x3 + 5x2 - 2x + 1;
If the marginal profit (in millions of dollars per year) is given byP′(t) = 2t - te-tuse an appropriate definite integral to find the total profit (to the nearest million dollars) earned over the
In Problem use absolute value on a graphing calculator to find the area bounded by the graphs of the equations over the given interval. Compute answers to three decimal places.y = -x3 + 7x2 + 5x - 9;
In Problem use absolute value on a graphing calculator to find the area bounded by the graphs of the equations over the given interval. Compute answers to three decimal places.y = e - x2; y = 0.1x +
A company manufactures downhill skis. It has fixed costs of $25,000 and a marginal cost given bywhere C(x) is the total cost at an output of x pairs of skis. Find the cost function C(x) and determine
In Problem use absolute value on a graphing calculator to find the area bounded by the graphs of the equations over the given interval. Compute answers to three decimal places.y = ln x; y = -1 +
Find the producers’ surplus at a price level of P ̅ = $67 for the price–supply equationp = S(x) = 10 + 0.1x + 0.0003x2
In Problem find the constant c (to two decimal places) such that the Lorenz curve f (x) = xc has the given Gini index of income concentration.0.63
Find the future value at 3.95%, compounded continuously, for 5 years of a continuous income stream with a rate of flow off (t) = 1,000 - 200t
In Problem find the constant c (to two decimal places) such that the Lorenz curve f (x) = xc has the given Gini index of income concentration.0.45
In Problem find the constant c (to two decimal places) such that the Lorenz curve f (x) = xc has the given Gini index of income concentration.0.27
Find the future value at 4.4%, compounded continuously, for 10 years for the continuous income stream with rate of flow f(t) = 50t2.Use Table 1 to evaluate all integrals involved in any solutions of
Problem refer to Figures A and B. Set up definite integrals in Problem that represent the indicated shaded areas over the given intervals.Over interval [a, c] in Figure B y = f(x) y = g(x) d a y =
In Problem evaluate each integral. V = dx x² - 36
In Problem illustrate each integral graphically and describe what the integral represents in terms of areas.Problem 21 In 2x dx
Problem refer to Figures A and B. Set up definite integrals in Problem that represent the indicated shaded areas over the given intervals.Over interval [b, d] in Figure B y = f(x) y = g(x) d a y =
In Problem evaluate each integral. Vx – 36 xp = .4
Problem refer to Figures A and B. Set up definite integrals in Problem that represent the indicated shaded areas over the given intervals.Referring to Figure B, explain how you would use definite
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem evaluate each integral. +4 x In (10 – x) dx 0.
In Problem evaluate each integral. | (In x)? dx
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem evaluate each integral. -2r хе dx
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = 2 - x; y = 0; 0 ≤ x ≤ 4
In Problem evaluate each integral. -2x
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = 2x - 1; y = 0; 0 ≤ x ≤ 1
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
A manufacturer warrants a product for parts and labor for 1 year and for parts only for a second year. The time to a failure of the product after it is sold is given by the probability density
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = x2 - 4; y = 0; -2 ≤ x ≤ 4
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = x2 - 1; y = 0; -1 ≤ x ≤ 2
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = x2 - 4x; y = 0; -1 ≤ x ≤ 4
Starting at age 25, you deposit $2,000 a year into an IRA account. Treat the yearly deposits into the account as a continuous income stream. If money in the account earns 5%, compounded continuously,
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = x2 - 6x; y = 0; -1 ≤ x ≤ 2
The weekly marginal revenue from the sale of x hair dryers is given byR′(x) = 65 - 6 ln(x + 1) R(0) = 0where R(x) is the revenue in dollars. Find the revenue function and the production level (to
In Problem find the area bounded by the graphs of the indicated equations over the given intervals (when stated). Compute answers to three decimal places.y = -2x + 8; y = 12; -1 ≤ x ≤ 2
Problem are mixed—some may require use of the integration by- parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula.
The rate of flow (in dollars per year) of a continuous income stream for a 5-year period is given byf(t) = 2,500e0.05t 0 ≤ t ≤ 5(A) Graph y = f(t) over [0, 5] and shade the area that represents

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