Business Decisions Sharon, the owner of the Brentwood Motel, is planning to renovate all the rooms in her motel. There are two plans before her. Plan A calls for an immediate cash outlay of $700,000, whereas plan B calls for an immediate outlay of $500,000. Sharon estimates that adopting plan A would yield an income stream of f(t) = 3,020,000e0'02t dollars/year for the next 5 years, whereas adopting plan B would yield an income stream of g(t) = 3,200,000 dollars/year for the next 5 years. If the prevailing rate of interest is 3%/year compounded continuously, which plan will yield the higher net income (in dollars) at the end of 5 years? 0 plan A (Q plan B Suppose the price of land in a city is given by the function 1 2 2 P(X,y) = 967 10 X E 15(y 1) where P(X,y) is the price of land at the point (x,y) in dollars per square metre and x and y are measured in kilometres. At what point within the city is the price of land highest? None of the other answers 0 (1,1) Flight of a Rocket. Suppose the altitude (in metres) of a rocket t seconds into flight is given by f(t) = -2+3 + 33t2 - 168t + 84 The interval where f(t) is concave down is 11 O O ( -00, 4 ) U (7 , 00 ) O ( 4, 7 ) O none of the other answers O (-00, 00) O -oo, 11 2Profit. Suppose the profit of a product is modelled by the function f(x) = 2x3 24x2 + 42x + 3 The absolute maximum value of f(x) on [2,8] is O f = 2 O f = -173 Q There is no maximum 0 r = 23 r=7 Or=-193 Suppose a person travels at a rate of 5 ft/hr toward the foot of a street lamp pole 63 ft high. The height of the person is 5.5 ft. At what rate is the distance from the head of the person to the top of the street lamp changing when 71 ft from the bottom of the street lamp? Note: Round your answer to 4 decimal places. 0 3.5983 ft/hr (9 3.7400 lm 0 0.2574 ft/hr O o ft/hr O -4 ft/hr O -o.2574 ft/hr 0 3.8856 ft/hr 0 none of the other answers