The U.S. Forever Stamp. The U.S. Postal Service sells the Forever Stamp, which is always valid as first-class postage on standard envelopes weighting 1 ounce or less, regardless of any subsequent increases in the first-class rate. (Source: U.S. Postal Service.) a. The cost of a first-class postage stamp was 4 ¢ in 1962 and 49 ¢ in 2014. This increase represents exponential growth. Write the function S for the cost of a 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 2016, 2018, and 2020. d. An advertising firm spent $4900 on 10,000 first-class postage stamps at the beginning of 2014. Knowing it will need 10,000 first-class stamps in each of the years 2015-2024, it decides to try to save money by also buying enough stamps to cover those years at the time of the 2014 purchase. Assuming there is a postage increase in each of the years 2016, 2018, and 2020 to the cost predicted in part (c), how much money will the firm save by buying the Forever Stamps in 2014? e. Discuss the pros and cons of the purchase decision described in Part (d).
The U.S. Forever Stamp. The U.S. Postal Service sells the Forever Stamp, which is always valid as first-class postage on standard envelopes weighting 1 ounce or less, regardless of any subsequent increases in the first-class rate. (Source: U.S. Postal Service.) a. The cost of a first-class postage stamp was 4 ¢ in 1962 and 49 ¢ in 2014. This increase represents exponential growth. Write the function S for the cost of a 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 2016, 2018, and 2020. d. An advertising firm spent $4900 on 10,000 first-class postage stamps at the beginning of 2014. Knowing it will need 10,000 first-class stamps in each of the years 2015-2024, it decides to try to save money by also buying enough stamps to cover those years at the time of the 2014 purchase. Assuming there is a postage increase in each of the years 2016, 2018, and 2020 to the cost predicted in part (c), how much money will the firm save by buying the Forever Stamps in 2014? e. Discuss the pros and cons of the purchase decision described in Part (d).
Solution Summary: The author calculates the exponential growth function of cost of a first-class stump, t years after 1962 if its value increased from 4 cents to 49
The U.S. Forever Stamp. The U.S. Postal Service sells the Forever Stamp, which is always valid as first-class postage on standard envelopes weighting 1 ounce or less, regardless of any subsequent increases in the first-class rate. (Source: U.S. Postal Service.)
a. The cost of a first-class postage stamp was
4
¢
in 1962 and 49
¢
in 2014. This increase represents exponential growth. Write the function S for the cost of a 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 2016, 2018, and 2020.
d. An advertising firm spent $4900 on 10,000 first-class postage stamps at the beginning of 2014.
Knowing it will need 10,000 first-class stamps in each of the years 2015-2024, it decides to try to save money by also buying enough stamps to cover those years at the time of the 2014 purchase.
Assuming there is a postage increase in each of the years 2016, 2018, and 2020 to the cost predicted in part (c), how much money will the firm save by buying the Forever Stamps in 2014?
e. Discuss the pros and cons of the purchase decision described in Part (d).
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