The U.S. Forever Stamp. On May 12, 2008, the U.S. Postal Service reissued the Forever

Chapter 3, Problem 29

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The U.S. Forever Stamp. On May 12, 2008, the U.S. Postal Service reissued the Forever Stamp (which features an image of the Liberty Bell). The Forever Stamp is always valid as first-class postage on standard envelopes weighing 1 ounce or less, regardless of any subsequent increases in the first-class rate. (Source: U.S. Postal Service.) a) The cost of first-class postage stamp was 4 in 1962 and 44 in 2010. This increase represents exponential growth. Write the function S for the cost of a stamp t years after 1962 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) An advertising firm spent $4400 on 10,000 first-class postage stamps in 2009. Knowing it will need 10,000 first-class stamps in each of the years 20102020, it decides at the beginning of 2010 to try to save money by spending $4400 on 10,000 Forever Stamps, but also buying enough of the 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 predicted in part (c), how much money will the firm save by buying Forever Stamps? e) Discuss the pros and cons of the purchase decision described in part (d).