PLEASE HELP!!!! i dont know how to do any of this! 52. Cigarette Consumpton The

Question

PLEASE HELP!!!! i dont know how to do any of this!

52. Cigarette Consumpton The data for the per capita con sumption of cigarettes over the last century is shown in the table, YearsPer Capita Cigarette Since 1900 Consumption 1976 4171 3851 2827 Sowree: Todacco Ownlook Report, Economie Research Service, US. Dept. of Agriculture a. Determine what type of mathematical model may best fit the data. Choose from linear, quadratic, or exponen- tial. Explain why you think the function you chose is the best choice. Be sure to justify your choice by show ing differences and ratios, the scatter plot, and what would seem most reasonable for the future. Defend v choice and refute the other two possibilities. b. Usc regression to find the function that best fits the data and name the function cv). c. Evaluate and interpret the real-world meaning of e09. d. Solve and interpret the real-world meaning of e(y) = 100. c. Using the function cy from part (b), approximate the year in which per capita cigarette consumption will each its maximum. f. Find the average rate of change from 1940 to 1950 and explain what your answer means in the context of this problem. Considering this decade, why would your answer seem reasonable?

Explanation / Answer

Notice that it increases upto 60
and then decreases

So, quadratic indeed

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b)
(0,54)
(10,151)
(20,665)
(30,1485)
(40,1976)
(50,3552)
(60,4171)
(70,3985)
(80,3851)
(90,2827)
(100,2092)

We get

y = -9.105011655·10-1 x2 + 125.274662 x - 821.6153846

As in
c = -0.9105y^2 + 125.2747y - 821.6154 ---> ANS

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c)
c(109) :
-0.9105(109)^2 + 125.2747(109) - 821.6154
2015.6764

As in, in the year 2009, oer capita cig consumption
would be 2016 approx

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d)
-0.9105y^2 + 125.2747y - 821.6154 = 100

Using quadratic formula,
we get y = 8 and y = 130 approx

So, in the years 1908 and 2030,
the per cap cig consumption was 100

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e)
c = -0.9105y^2 + 125.2747y - 821.6154

Using y = -b/(2a),
we get -125.2747/(2*-0.9105)
68.7944535969247666

As in y = 69 approx

So, in the year 1969, the per cap consumption
reached its max

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f)
(3552 - 1976) / (10)
157.6

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