Question: (a) Let V (x) denote the number of litres of fuel left in an aircraft's fuel tank if it has flown x km. Suppose that V (x) satisfies the following differential equation:
V'(x) = -aV(x) - b
(The fuel consumption per km is a constant b > 0. The term -aV(x), with a > 0, is due to the weight of the fuel.) Find the solution of the equation with V(0) = V0.
(b) How many km, x∗, can the plane fly if it takes off with V0 litres in its tank?
(c) What is the minimum number of litres, Vm, needed at the outset if the plane is to fly x^ km?
(d) Put b = 8, a = 0.001, V0 = 12 000, and x^ = 1200. Find x∗ and Vm in this case.