Problem 8a: Algebraically show that A zine-RI if and only if h1[A] versus T is linear. Find the slope, m, and the vertical intercept, d, in terms of P and R. ELBetty and Bob have an account that is growing approximately exponentially. The account value, A, versus the time, T, in years is given by the following table of partial in-uts and out uts: 8 6200 r000 11 500 1a 400 19 000 Find the equation of the Least Squares Line of 111m.) versus T. Using part 8a algebraically predict A for T = 10. What is the approximate rate of return, R, and the principal, P? Your final numerical answers should be accurate to 3 places after the decimal point. Problem 9: Betty and Bob seek treasure and adventure at a dessert oasis. Each unit of (gold, jewels, coins) is Worth ($2 million, $3 million, $2 million) and Takes {1 hour, 2hours, 2 hours) to find and Weighs (2 pounds, 1 pound, 2 pounds) and Occupies {2 units, 1 unit, 1 unit) of space. If they have at most 14 hours to seek, can carry at most 20 pounds, and have at most 16 writs of space then find the number of units of gold, jewels, and coins that would maximize the value of the treasure. What is this maximum value? Use the Simplex Method as detailed in the appendix Linear Programming 8.: the Simplex_ Method. Be sure to show all your tableau work