Math 135 April 22, 2013 Writing Assignment 2 The central focus of this writing assignment is solving and presenting the solution of the following integration application problem: Your task is to carefully present this solution in the context of a detailed explanation of your work. Your explanation should be directed to a Math 135 student who has been challenged by this problem and does not understand the setup or the mathematics of your solution. You will soon surmise that you will be applying some of the material from section 5.2 in our text. In part (a), you will need to use both equations (5) and (6) from that section. A portion of your presentation should be an explanation of why equation (5) is valid, i.e., you should include an explanation of why the Riemann sum ? ? ?? ? n i kt i R t e i t 1 approximates the accumulated future value of Sam’s investments in the case where R(t) is constant and leads to equation (5) (hint: see the discussion on pp. 481 and 482). Equation (6) is valid in this case in part (a) where R(t) is constant (include details), but in fact, is not valid in the case where R(t) is not constant, as in the case of part (b). In this setting, you will need the result that ? ? ? ? . 0 A R t e dt k T t T ? ? ? Again you should include a Riemann sum argument that justifies this more general result. That is, you need to explain why the Riemann sum ? ? ?? ? ? n i k T t i R t e i t 1 ( ) is an approximation for the accumulated future Sam is a 22 year old CSUF finance major who recently graduated and was just hired by a prestigious insurance company. Sam is thinking ahead and plans to invest part of his weekly wage into his personal investment account. (a) If the amount that he invests is constant and if Sam wants his account to be worth $1,000,000 when he is 69 years old, how much should he invest each week? Assume that the account will earn 6% annual interest compounded continuously and that Sam’s investment will go into the account as a continuous…