Download Fall 2005 Test 2 Form A: Mathematics Problems with Differential Equations and Integrals - and more Exams Mathematics in PDF only on Docsity! 1526 Fall 2005 Test 2 Form A Name (printed)____KEY___________ Section______________ Do work on test sheet. No electronic device or other helps may be used. Part 1 Circle one of the choices as your choice of answer in each of the following problems. You may use the test sheet as scratch paper, but only the circled choice will be considered as the answer. Each problem in this part is worth 5 points. 1. Your sales for your the Hokie Hums CD are falling at an instantaneous rate of 6% per month. If you are currently selling 200 CD’s a month, find the differential equation and the point used to predict future sales. Let S(t) be the number of sales of CD’s at time t months from now. Gave partial credit if choose c since the point and units were correct. a. 0.06 sales/month point (0, 200)SdS dt = − b. 200 0.06 dollars/month point (0, 0)dS t dt = − + c. 200 0.06 sales/month point (0, 200)SdS dt = − d. 0.06 dollars/month point (0, 200)dS t dt = − 2. Your company just introduced a new Hokie Hat to the campus market. You predict you will eventually sell 30,000 and that your monthly rate of sales will be 10% of the difference between the saturation level and the total sales to that point. Find the differential equation and the point used to predict future sales. Let S(t) be the sales in number of hats at time t months from now. a. ( )0.1 30,000 sales/month point (0,10)dS S dt = + b. ( )10 30,000 dollars/month point (0,0)dS S dt = − c. ( )0.1 30,000 sales/month point (0,0)dS S dt = − d. ( )10 30,000 dollars/month point (0,10)dS S dt = − 3. The formula for the total value of a continuous income stream when rate of receipt of income from time t = a to time t = b is R(t) dollars per year at APR of ( r)(100%) is: a. ( )( ) b r b t a R t e dt−∫ b. ( ) b a R t dt∫ c. ( )( ) b r a t a R t e dt−∫ Over. 4. The owners of a small airline hope to be able to buy out a larger airline 10 years from now. They have determined that they can afford to invest $3.3 million each year in an account that returns 19.4% APR. Assuming a continuous income stream, SET UP the integration to show how much the the account will be worth in 10 years? a. 10 19.4(10 ) 0 3.3 te dt million dollars−∫ b. 10 0 3.3dt million dollars∫ c. 10 0.194(0 ) 0 3.3 te dt million dollars−∫ d. 10 0.194(10 ) 0 3.3 te dt million dollars−∫ 5. Using the graph below, circle the set up for the AREA between the curves on the x interval [-5, 0]. -25 -20 -15 -10 -5 0 5 10 -5 -4 -3 -2 -1 0 1 2 3 4 5 x y f (x) g(x) A. ( )( )0 25 6x x dx− − −∫ B. ( )( ) ( )( ) 3 02 2 5 3 6 6x x dx x x dx − − − − − + − −∫ ∫ C. ( )( )0 25 6 x x dx− − −∫ D. ( )( ) ( )( ) 3 02 2 5 3 6 6x x dx x x dx − − − − − + − −∫ ∫ 6. If Consumers’ Surplus = ( ) 100 0 ( ) 20 $400,000D q dq− =∫ , then the correct interpretation is: a. The consumers each save an extra $400,000 when selling at the equilibrium price of $100. b. The consumers as a group save an extra $400,000 when buying at the equilibrium price of $20. c. The consumers each earn $400,000 when buying at the equilibrium price of $100. d. The consumers as a group earn an extra $400,000 when selling at the equilibrium price of $20. Threw out #6. 7. If social gain for a particular product is $ 10 million dollars and producers’ surplus is $7 million dollars, then how much is consumers’ surplus? a. 17 million dollars b. 3 million dollars c. Not enough information given to solve the problem. Next page.
