Question

a) The cost of first-class postage stamp was 44 in 1965 and 40e in 2010. This increase represents exponential growth. Write the function S for the cost of a stamp tyears after 1965 (1-0) b) What was the growth rate in the cost? c) Predict the cost of a first-class postage stamp in 2019, 2022, and 2025, d) 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 An advertising firm spent $4000 on 10,000 first-class postage stamps in 2009 Knowing it will need 10.000 first-class stamps in each of the years 2010-2026, it decides at the beginning of 2010 to try to save money by spending $4000 on 10,000 Forever Stamps, but also buying enough of the stamps to cover the years 2011 through 2026. Assuming there is a postage increase in each of the years 2019, 2022, and 2025 to the cost predicted in part (c), how much money will the firm save by buying the stamps? a) Choose the correct answer below. OA S1)=0.05 B St)-4 5(0)=0 05 b) The growth rate is approximately 5%. (Round to the nearest integer as needed.) The cost of a first-class postage stamp in 2019 is 60 (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 2022 is 69 (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 2025 is 80 e (Use the answer from part (a) to find this answer Round to the nearest integer as needed) d) The firm will save 5 by buying the stamps at the beginning of 2010

Answer 1

The task involves finding an exponential function for stamp cost over time, determining the growth rate, predicting future costs, and calculating savings from purchasing Forever Stamps. The presented figures seem to have typos and require clarification for precise calculations.

Step-by-step explanation:

The student has asked to find a function S(t) representing the cost of a first-class postage stamp t years after 1965, with known costs in 1965 and 2010. This is followed by determining the growth rate, predicting future costs and calculating potential savings with the Forever Stamp.

Exponential Growth Formula

Given the costs in 1965 (44 cents) and 2010 (40e cents), which indicate an exponential growth, the general form of the exponential function is S(t) = a * e(rt). The equation is solved using the given values, where a is the initial amount, r is the growth rate, and t is time.

Growth Rate Calculation

The growth rate r can be found by using the two known cost values for 1965 and 2010, and then can be used to predict costs for future years. The apparent misprint of costs as '44' and '40e' makes it challenging to provide accurate calculations without the correct figures.

Savings Calculation

To calculate the savings from purchasing Forever Stamps, one would need to compare the costs of using Forever Stamps against the costs of stamps in subsequent years. Assumptions are made regarding price increases based on the predicted costs from part c.