Find the accumulated future value of the continuous income stream at rate R(t), for the given time T, and interest rate k, compounded continuously. R(t) = $40,000, T = 23 years, k = 5% The accumulated future value is 39 (Round to the nearest ten dollars as needed.) A clothing company determines that its marginal cost, in dollars per dress, is given by the function below. Find the total cost of producing the rst 210 dresses, disregarding any fixed costs. 3 C'(x) = - EX + 48, for x s 450 The total cost is $ . (Round to the nearest cent as needed.) Find the future value P of the amount P0 = $200,000 invested for time period t= 2 years at interest rate k = 4%, compounded continuously. If $200,000 is invested, what is the amount accumulated after 2 years? 35 (Round to the nearest cent as needed.) Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x) = kx2, [ 2,5] k = (Type an exact answer.) The probability density function is f(x) = . (Type an exact answer.) Find the area of the region bounded by the graphs of the given equations. y = x, y= 21x The area is. (Type an integer or a simplified fraction.)