Directions: Show all your work. Any answer with less than sufcient supporting work may be awarded less than full credit. Part A. Rational Functions 1. Based on data from the US. Department of Agriculture. the average number of acres per farm x years after 2000 can be approximated by the model 2078x 94458 A{x) _ = 13:4 2164 a. Use the model. to estimate the average number of acres per farm :in 2005. b. Use the model to predict the average number of acres per farm in 2012. c. Find and interpret the zero of the rational function. Does this result make sense within the context of the problem? Part B. Applications of Exponential Functions 2. Lynsey invests S3000 in a bond trust that pays 8% interest compounded semiannually. Her friend Lyla. invests $3000 in a certicate of deposit that pays ?.?5% compounded monthly. who has more money after 20 years, Lynsey or Lyla? Part C. Arithmetic Sequences 3. A brick staircase has a total of 40 steps. The bottom step requires 88 bricks. Each successive Step requires two less bricks than the prior step. a. How many bricks are required for the top step? b. How many bricks are required to build the staircase? 1 Part D. Geometric Sequences 4. Suppose someone offers Melissa a job to work for 30 days. On the first day she will be paid 1$, on the second day 24, on the third day 4, on the fourth day 8, etc. If Melissa take the job, how much is her total pay for the 30 days?Part E. Applications of Matrices [Solving Systems of Linear Equations] 5. A nutritionist in a nursing home is to arrange a special diet composed of three basic foods. The diet is to include exactly 340 units of calcium, 180 units of iron, and 220 units of vitanlin A. The number of units per ounce of each special ingredient for each of the foods is indicated in the table below. How many ounces of each food must be used to meet the diet requirements? Units per Ounce food I food 11 food III total units Calcium 30 10 20 340 Iron 10 10 20180 VitaminA IO 30 2C] 220 a. Identify the variables of the problem using 3:. y and z. b. Determine the system of equations to be solved. c. Write the Augmented Matrix for the system of linear equations then solve using determinants. You can use the calculator to solve it. Write all determinants for the matrix. x. y. and z. Use 13 rop er notation