The following table relates the weight of garbage in tons to the time in years since 1984. It is known that the relationship is exponential. Use the table to answer the following questions. Number of years since 198413579Weight of garbage (in tons)25803715.25349.8887703.8387211093.52776What is the 2-year growth factor? What is the 1-year percent change? What was the weight of the garbage in 1982?

Consider the provided question, Let f(t) be the weight of the garbage after t years which is exponentially given as, f(t)=CektFrom the table, at t=1, f(1)=2580⇒2580=Cek ......(I)From the table, when t=3, f(3)=3715.2⇒3715.2=Ce3k ......(II) Divide the equation (II) by (I), we get, 3715.22580=Ce3kCek⇒3715.22580=e2k⇒ln3715.22580=lne2k⇒ln3715.22580=2k1⇒k=ln3715.225802=0.1823From (I),2580=Ce0.1823⇒C=2580e0.1823≈2150Since, f(t)=Cekt⇒f(t)=2150e0.1823t(1) Find the 2 year growth factor. The growth factor=ektSo, the 2 years growth factor=e0.18232=1.4399(2) Find the 1 year percentage change, 1 year percentage change=Increase of weight in 1 yearInitial weight×100=2580-21502150×100=20% (3) Find the weight of the garbage in 1982. Weight of garbage in 1982=Weight in 1984Growth factor for 2 years=21501.4399=1493.16So, Weight of garbage in 1982 is 1493.16 tons

Answered: The following table relates the weight…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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The following table relates the weight of garbage in tons to the time in years since 1984. It is known that the relationship is exponential. Use the table to answer the following questions.

Number of years since 1984	1	3	5	7	9
Weight of garbage (in tons)	2580	3715.2	5349.888	7703.83872	11093.52776

What is the 2-year growth factor?
What is the 1-year percent change?
What was the weight of the garbage in 1982?

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