6)

Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish, was modelled by the equation 4x + 12 f (t ) = x* + 6x + 3 where t is measured in years and A(t) in kilograms per year. Consider the integral 4x + 12 1 dx x2 + 6x + 3 After substitution into u, the new integral can be written (a) The value of A is Ox+ 3 O x O2 O 4X O 12 0 4 O 4x + 3 (b) The upper limit of integration b is O 10 0 4 O 1 O 60 O 20 O 30 O -10 O -30Business 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 $900,000, whereas plan B calls for an immediate outlay of $200,000. Sharon estimates that adopting plan A would yield an income stream of f(t) = 3,060,00090.03t 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 4%/year compounded continuously, which plan will yield the higher net income (in dollars) at the end of 5 years? O plan A O plan B