Mathematics For Biz and Econ Integration Reading: Jacques: Chapter 6 Lecturer: Mr. Anh Vu, CMA, MSA 11/22/2021 Prepared by Anh Tuan Vu 1 1. 2. 3. 4. 5. 6. Definition of an integral Rules for integration Application I – Revenue, Costs and Profit Definite Integration Application II – Investment Flow Application III – Discounting 11/22/2021 Prepared by Anh Tuan Vu 2 11/22/2021 Prepared by Anh Tuan Vu 3 11/22/2021 Prepared by Anh Tuan Vu 4 11/22/2021 Prepared by Anh Tuan Vu 5 11/22/2021 Prepared by Anh Tuan Vu 6 11/22/2021 Prepared by Anh Tuan Vu 7 11/22/2021 Prepared by Anh Tuan Vu 8 11/22/2021 Prepared by Anh Tuan Vu 9 11/22/2021 Prepared by Anh Tuan Vu 10 11/22/2021 Prepared by Anh Tuan Vu 11 11/22/2021 Prepared by Anh Tuan Vu 12 11/22/2021 Prepared by Anh Tuan Vu 13 11/22/2021 Prepared by Anh Tuan Vu 14 11/22/2021 Prepared by Anh Tuan Vu 15 11/22/2021 Prepared by Anh Tuan Vu 16 11/22/2021 Prepared by Anh Tuan Vu 17 11/22/2021 Prepared by Anh Tuan Vu 18 11/22/2021 Prepared by Anh Tuan Vu 19 11/22/2021 Prepared by Anh Tuan Vu 20 11/22/2021 Prepared by Anh Tuan Vu 21 11/22/2021 Prepared by Anh Tuan Vu 22 11/22/2021 Prepared by Anh Tuan Vu 23 11/22/2021 Prepared by Anh Tuan Vu 24 • In Chapter 3 the formula P = Se-rt/100 was used to calculate the present value, P, when a single future value, S, is discounted at r% interest continuously for t years. • If the fund is to provide a continuous revenue stream for n years at an annual rate of S dollars per year then the present value can be found by evaluating the definite integral 11/22/2021 Prepared by Anh Tuan Vu 25 11/22/2021 Prepared by Anh Tuan Vu 26 11/22/2021 Prepared by Anh Tuan Vu 27 Q1: • A firm’s marginal revenue and marginal cost functions are given by MR = 240 − 0.6Q2 and MC = 150 + 0.3Q2 • If fixed costs are 50, determine the maximum profit ? 11/22/2021 Prepared by Anh Tuan Vu 28 Q2 • If the net investment function is given by I(t) = 100 e0.1t • calculate (a) the capital formation from the end of the second year to the end of the fifth year (b) the number of years required before the capital stock exceeds $100 000. 11/22/2021 Prepared by Anh Tuan Vu 29 11/22/2021 Prepared by Anh Tuan Vu 30
