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).
Anthony bought a car at a price lf $25,520 in the year 2005. The price of the car depreciates at abrate of 5% annualy. Which functions describe the price lf the car t years after 2005?
Write the explicit function that represents this bank account.
A minivan is purchased for $29,248. The value of the vehicle depreciates over time.
Describe the advantages and disadvantages of using a linear function to represent the depreciation of the car over time.
Describe the advantages and disadvantages of using an exponential function to represent the depreciation of the car over time.
The minivan depreciates $3,000 in the first year. Write either a linear or exponential function to represent the value of the car x years after it was sold.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY