An economist models the output of a farm using the Solos.r model: This model gives the output PH} 2 [l of the farm in terms of the value of its equipment Q(t) E [l by Pm = am): It is assumed that the equipment depreciates at a constant rate cl 2::- 0 and that a constant fraction [1 s: r a: 1 of the output is reinvested into equipment. This leads to the ODE Q 2 TP 5122. (a) Sketch a phase portrait for P, indicating the location and stability of any xed points. (b) 1n suitable units, the depreciation rate of a certain farm's equipment is E = 4; and the initial value of its equipment is 122(0) 2 3. If its production initially decreasesI what can you say about the rate of investment 1'? (c) After many years, a second farm is observed to have essentially the same output as the rst farm. It is known that its rate of investment is r : %. What can you say about the rate of depreciation of the second farm's equipment