\f5. a, =4a, 1 4a,_;, ay =2, a; = 10 The population of Utopia increases 5 percent per year. In 2000 the population was 10,000. What was the population in 1970? 7. Write a non-recursive version of the binary search algorithm.. If a person invests in a tax-sheltered annuity, the money invested, as well as interest earned, is not subject to taxation until withdrawn from the account. Assume a person invest $2000.00 each year in a tax-sheltered annuity at 10 percent interest compounded annually. Let A represent the amount at the end of n years. a. Find the recurrence relation for the sequence A, A A,.... b. Find an initial condition for the sequence A .A A,.... c. Find A, A, and A,. d. Find and explicit formula for A . How long will it take for a person to double the initial investment? Solve the following recurrence relations for the initial conditions given. 2. a, =-3d,-1 , do =2 3. a = 2nd, _ , do =1