a) Yt+1 = 2yt - 10 b) Yt+1 = Yt c) ye = 0.5yt-1+1 %3D
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- The shiver-me-Timbers tree farms has 7,800 lumber-quality fast growing trees that are ready to be harvested. The company has a strategy that each year it will harvest 12% of the trees and plant 660 lumber-quality trees during the year. Let n represent the number of years and Yn represent the number of lumber-quality trees on the farm at the end of the year. A) Form the difference equation and initial value that models the timber company's strategy where Yn represent the number of lumber-quality trees on the farm at the end of the year and Yn-1 represent the number of lumber-quality trees on the farm at the end of the previous year. B) solve the difference equation. C) use the solution of the difference equation to find Y36. D) Interpret the results for part c. E) According to the difference equation model, will the tree farm ever reach a point in the future when you have no trees harvest?Indicate the transient portion and steady state portion of the solution y=-e- e2t does the solution behave in the long term? and how + 3 3Solve each of the following initial value problems. Describe in a few words how the solutions resemble, and differ from each other. dy (a) = 2y4, y(0) = yo dt dy (b) 4y - 4, y(0) = Yo dt dy (c) 4y - 8, y(0) Yo dt Choose one = = =
- )ANTHONY HAS INHERITED $10,000 AND DECIDES TO INVEST IT. HE HAS FOUND SEVERAL DIFFERENT OPTIONS AT LOCAL BANKS, AND NOW NEEDS TO SEE WHICH ONE WILL EARN HIM THE MOST ON HIS INVESTMENT, OPTION 1: 8% ANNUALLY OPTION 2:5.5% QUARTERLY OPTION 3:6%, CONTINUOUSLY A. HoW MUCH WILL HE HAVE IN THE ACCOUNT AFTER 5 YEARS IF HE CHOOSES THE FIRST OPTION? B. How MUCH WILL HE HAVE IN THE ACCOUNT AFTER 5 YEARS IF HE CHOOSES THE SECOND OPTION? C. HoW MUCH WILL HE HAVE IN THE ACCOUNT AFTER 5 YEARS IF HE CHOOSES THE THIRD OPTION? D. USE YOUR CALCULATIONS FOR PARTS A-C TO DETERMINE WHICH IS THE BEST OPTION FOR ANTHONY, EXPLAIN YOUR CHOICE. E. HOW LONG WILL IT TAKE FOR HIS INVESTMENT TO TRIPLE IN VALUE WITH THE OPTION YOU CHOSE? WRITE YOUR ANSWER IN TERMS OF YEARS AND MONTHS.Consider the basic macroeconomic model: Y=C+I and C = a + by where Y is GDP, C is consumtion and I is total investment (treated as fixed). a, b are positive parameters. Solve the model for Y in terms of I and the parameters.Early Monday morning, the temperature in the lecture hall has fallen to 41°F, the same as the temperature outside. At 7:00 A.M., the janitor turns on the furnace with the thermostat set at 72°F. The time constant for the building is 1 1 2 -= hr. K₁ 3 = 3 hr and that for the building along with its heating system is K Assuming that the outside temperature remains constant, what will be the temperature inside the lecture hall at 8:30 A.M.? When will the temperature inside the hall reach 67°F?
- 1 Early Monday morning, the temperature in the lecture hall has fallen to 41°F, the same as the temperature outside. At 7:00 A.M., the janitor turns on the furnace with the thermostat set at 72°F. The time constant for the building is =3 hr and that for the building along with its 1 1 heating system is =hr. Assuming that the outside temperature remains constant, what will be the temperature inside the lecture hall at 8:00 A.M.? When will the temperature inside the hall reach 70°F? K₁ At 8:00 A.M., the temperature inside the lecture hall will be about°F. (Round to the nearest tenth as needed.) CIn a hybrid-engine vehicle, energy from battery (“b" in Amperes) and from 95 octane unleaded gasoline ("g" in liters) are used intermittently to maximize the distance to be travelled (mileage) between fill- ups and charge-ups. If mileage (M) in kilometers is found out to be: M= 90 b+ 100 g - 3 b' - 5 g? - 2 b g find the values of “b" and “g" that will maximize mileage M, find the maximum mileage and prove that this is a maximum.Assume that an open economy with a floating exchange rate is described by the equations:C = 0.5(Y-T)T= 1000I= 1500 -250rG= 1500NX= 1000 – 250e(M/P)d = 0.5Y – 500rM= 1000S-I= 500 – 250rP= 2r* = 1 a. Solve for NX and e. b. Using the information from parts a. to be part d. above, graphically illustrate on aclearly labelled diagram, the short-run impact of contractionary fiscal policy on theexchange rate and level of output in this small open economy.c. Assuming that the economy adopted a fixed exchange rate system, illustrate on aclearly labelled diagram, the impact of contractionary fiscal policy.
- b. Find the equilibrium quantity.Solve the following B.V.P. utt %3D с 2ихx; { и(х, 0) 3D сos x — и (0д) %3 0, и(2п,) - 00C. The quoted value of AGB=GB-G₁ = -1.43 kJ/mol corresponds to a-D-glucose ending in a state of 100 % B-D-glucose, meaning Ginitial = Ga while the Gfinal = Gg. If instead only a fraction x ends up as B-D-glucose while the rest (1-x) ends as a-D-glucose then Gfinal = xGB + (1-x)Ga 1. Use this to find AG if, starting with 100% a-D-glucose only of it ends up as the 3-D form.SEE MORE QUESTIONS
