15. Suppose that in 1667, a man bought a diamond for $37. Suppose that the man had instead put the $37 in the bank at 3% interest compounded contin would that $37 have been worth in 2005? In 2005, the $37 would have been worth $ Do not round until the final answer. Then round to the nearest dollar as needed.) 16. a) The cost of first-class postage stamp was 70 in 1962 and 704 in 2010. This increase represents exponential growth. Write the function S for the stamp t years after 1962 (t = 0). b) What was the growth rate in the cost? C) Predict the cost of a first-class postage stamp in 2013, 2016, and 2019. d) The Forever Stamp is always valid as first-class postage on standard envelopes weighing 1 ounce or less, regardless of any subsequent increase first-class rate. An advertising firm spent $7000 on 10,000 first-class postage stamps in 2009. Knowing it will need 10,000 first-class stamps in years 2010-2020, it decides at the beginning of 2010 to try to save money by spending $7000 on 10,000 Forever Stamps, but also buying enough stamps to cover the years 2011 through 2020. Assuming there is a postage increase in each of the years 2013, 2016, and 2019 to the cost predi (c). how much money will the firm save by buying the stamps? a) Choose the correct answer below. O A. S(1) =7g Kt O B. S(1) = 0.05 2 71 O C. S(1) = 7 0.ost O D. S(1) = 0.05 2 701 b) The growth rate is approximately %. (Round to the nearest integer as needed.) c) The cost of a first-class postage stamp in 2013 is Use the answer from part (a) to find this answer. Round to the nearest integer as needed.) The cost of a first-class postage stamp in 2016 is Use the answer from part (a) to find this answer. Round to the nearest integer as needed.) The cost of a first-class postage stamp in 2019 is (Use the answer from part (a) to find this answer. Round to the nearest integer as needed.) d) The firm will save $ by buying the stamps at the beginning of 2010. Use the answers from part (c) to find this answer.) 17. Suppose that a company introduces a new computer game in a city using television advertisements. Surveys show that P% of the target audience bu after x ads are broadcast, satisfying the equation below. Complete parts (a) through (d). 100 P(x) = - 1+48 e - D.1x a) What percentage buy the game without seeing a TV ad (x = 0)? Type an integer or a decimal rounded to the nearest tenth as needed ) b) What percentage buy the game after the ad is run 50 times? (Type an integer or a decimal rounded to the nearest tenth as needed.) c) Find the rate of change, P'(x). P'(x) = d) Sketch a graph of the function. Choose the correct graph below. O A. OB O C. OD Q P(X) 100- 100- 100- Q Q 18. The size of a certain insect population is given by P(t) = 400e .0it, where t is measured in days. At what time will the population equal 2400? It will take days for the population to equal 2400. (Round to one decimal place as needed.)