Section 3.6: (page 211) Numbers 6-13 all Section 3.7: (page 218) whole page Section 3.8: (page 227) Numbers 1-13 oddw

textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (ONL) X BusCalc.pdf X *Dashboard X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks BusCalc.pdf 211 / 272 69% + Chapter 3 The Integral Business Calculus 211 3.6 Exercises In problems 1 - 4, use the values in the table to estimate the areas. f (x g(x) h(x) 209 3 6 2 N W A a a un 5 6 1. Estimate the area between fand g, between x = 0 and x = 4. 2. Estimate the area between g and h, between x = 0 and x = 6. 3. Estimate the area between fand h, between x = 0 and x = 4. 4. Estimate the area between fand g, between x = 0 and x = 6. Island 5. Estimate the area of the island shown - 340 feet_ _- 410 feet - 220 feet 240 feet_ In problems 6 - 15, find the area between the graphs of f 210 and g for x in the given interval. Remember to draw the graph! - 100 6 6. f(x) =x2 + 3, g(x) = 1 and -1 Sx$2. 7. f( x) = x2+3, g(x) = 1 + x and OSx53. 8 . f( x ) = x2 , g(x ) = x and 0Sx52. 9 . f ( x ) = ( x -1)2 , g(x) = x + 1 and OSx53. 10. f(x) = > , g(x) =x and 1 SxSe. 1 1. f(x) = Vx , g(x) =x and 0 Sx 54. 217 12 . f ( x ) = 4 -x 2, g(x) = x + 2 and OSx52. 13 . f (x ) = et , g(x) = x and OSx52 O 14 . f(x ) = 3 , g(x) = V/1 -x2 and OSx51. 15 . f(x ) = 2, g(x) = V/4-x2 and -25x $2. I'M 212textbroker.com X Final Exam X X Canvas LMS X MATH140-12141 (0 X BusCalc.pdf X *Dashboard X Meeting 19 - Chapt X - CD A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks BusCalc.pdf 218 / 272 69% + Chapter 3 The Integral Business Calculus 218 From t = 0 to t = 1 (the first year), the income is constant $7000 per year. From t = 1 to t = 8, the income is increasing by $800 each year; the income flow function F(t) will be F(t)=7000 + 800(t -1)= 6200 + 800t. To find the present value, we'll have to divide the integral into the two pieces, one for each of the functions: 216 PV = [7000e 017'dt + (6200 + 800t)e 0.017'dt = 70166. The present value is greater than the cost of the machine, so the company should buy the machine. 3.7 Exercises 1. The demand and supply functions for a certain product are given by p = 150-.5q and p =.002q2 +1.5, where p is in dollars and q is the number of items. (a) Which is the demand function? (b) Find the equilibrium price and quantity 217 (c) Find the total gains from trade at the equilibrium price. 2. Still thinking about the product from Exercise 1, with its demand and supply functions, suppose the price is set artificially at $70 (which is above the equilibrium price) a) Find the quantity supplied and the quantity demanded at this price. (b) Compute the consumer surplus at this price, using the quantity demanded (c) Compute the producer surplus at this price, using the quantity demanded (why?). (d) Find the total gains from trade at this price. (e) What do you observe? 3. When the price of a certain product is $40, 25 items can be sold. When the price of the same product costs $20, 185 items can be sold. On the other hand, when the price of this product is $40, 200 items will be produced. But when the price of this product is $20, only 100 items will be produced. Use this information to find supply and demand functions (assume for simplicity that the functions are linear), and compute the consumer and producer surplus at 218 the equilibrium price. 4. Find the present and future values of a continuous income stream of $5000 per year for 12 years if money can earn 1.3% annual interest compounded continuously. 5. Find the present value of a continuous income stream of $40,000 per year for 35 years if money can earn (a) 0.8% annual interest, compounded continuously, (b) 2.5% annual interest, compounded continuously (c) 4.5% annual interest, compounded continuously. 219textbroker.com X -Final Exam X X Canvas LMS X MATH140-12141 (0 X BusCalc.pdf X *Dashboard X Meeting 19 - Chapt X -> C A Not Secure | opentextbookstore.com/buscalc/BusCalc.pdf Update : Suggested Sites M Gmail YouTube Disney+ canvas find cards saved o... Other Bookmarks E BusCalc.pdf 228 / 272 69% + 3.8 Exercises 225 In problems 1 -4, check that the function y is a solution of the given differential equation. 1. y' + 3y = 6. y=e-3X +2. 2. y' - 2y =8. y=e2X -4. 3. y' =-x/y. y= V7-x2 . 4. y' = x-y. y=x-1+2e-* . 226 Chapter 3 The Integral Business Calculus 228 In problems 5 -8 check that the function y is a solution of the given initial value problem. 5. y' = 6x2 - 3 and y(1) =2. y= 2x5 - 3x + 3. 5. y' = 6x + 4 and y(2) =3. y=3x2+ 4x - 17. 7. y' = by and y(0) =7. y= 75x 8. y' =-2y and y(0) =3. y= 3e-2x 227 In problems 9- 12, a family of solutions of a differential equation is given. Find the value of the constant C so the solution satisfies the initial value condition. 9. y' = 2x and y(3) =7. y =x2+ C. 10. y' = 3x2- 5 and y(1) = 2. y = x3 - 5x + C. 11. y' = 3y and y(0) = 5. y = Ce3x 11. y' =-2y and y(0) = 3. y = Ce-2x In problems 13 - 18, solve the differential equation. (Assume that x and y are restricted so that division by zero does not occur.) 13. y' = 2x 14. y' = x/y 15. xy' = y + 3 228 16 . y' = x y + 3y 17. y' = 4y 18. y' = 5(2 -y) In problems 19-22, solve the initial value separable differential equations. 19. y' = 2xy for y(0) = 3, y(0) = 5, and y(1) = 2. 20. y' = x/y for y(0) = 3, y(0) = 5, and y(1) = 2. 21. y' = 3y for y(0) = 4, y(0) = 7, and y(1) = 3. 22. y' =-2y for y(0) = 4, y(0) = 7, and y(1) = 3. 23. The rate of growth of a population P(t) which starts with 3,000 people and increases by 4% per year is P '(t) = 0.0392-P(t). Solve the differential equation and use the solution to estimate the population