1) [2 points each] Simplify the following (= Write them with a single exponent.) a ) (p-3) ( 4) b) p12 = p+ 2) Solve for j. Round your answer to the nearest .001 1 - 8 = 27) [2 points each] The first three terms in an infinite geometric series are 42, 31.5, and 23.625. a) Find g13. Round to the nearest .0001 . b) Find the sum of this infinite geometric series. 8) The total number of people who have seen a band play as of the 1*' of each month follows a geometric sequence. As of March 1, a total of 6,100 people have seen the band perform. As of July 1 of that same year, a total of 8,450 people have seen the band perform. Assuming this pattern continues, how many people will have seen the band perform as of April 1 of the following year? Round your answer to the nearest person. 9) %13,000 is deposited into a well-run bond fund, which pays an annual yield of 5.4%. The average inflation rate is 3.2%. a) What is the (nominal) value after 9 years? Round down to the nearest penny. b) How much real interest has been earned after 9 years? Round to the nearest dollar. 10) True fact: Ancient Roman contractors who built roads were paid half when the road was completed, and half 40 years after the road had been completed if the road was still in good working order. Assume the annual yield is 1.625%. A contractor receives a contract to build a small road and will be paid a total 12,000 denarii. It will take 3 years to complete the road, so the contractor will be paid 5,000 denarii in 3 years and another 5,000 denarii in 43 years. What (to the Ancient Roman contractor) is the present value of this contract? Round your answer to the nearest denarii. 11) After a weekend of lucrative gigs, a singer finds herself with an extra 31,500. She currently has 34,350 of credit card debt, on which she is charged an annual yield of 19%. Putting *1,500 toward this would cut that debt to 32,850. Calculate the annual rate of return if she does this. Round, if necessary, to the nearest 0.1%