Question 1- Find the accumulated present value of each continuous income stream at rate R(t), for the given time T and interest rate k, compounded continuously.
R(t) = 0.07t + 100, T = 10, k = 5%
Question 2- A coffee company has found that the marginal cost, in dollars per pound, of the coffee it roasts is represented by the function below, where x is the number of pounds of coffee roasted. Find the total cost of roasting 150 lb of coffee, disregarding any fixed coasts.
C'(x) = -0.027x + 6.25, for x ≤ 200.
Question 3- Find the under the graph of the function over the interval given.
f(x) = ex; [-5, 3].