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The per capita consumption of commercially produced fresh vegetables in a certain country from 1980 through 2000 was as shown in the accompanying table.Per capita consumption of fresh vegetablesin a certain countryVegetable consumption, V(pounds per person)Year1980147.119851571990167.11995176.1200.72000(a) Find the function of the quadratic model that gives the per capita consumption of fresh vegetables in pounds per person, where t is the number of years since 1980, with data from 0 sts 20. Examine the equation graphed on a scatter plot of the data(Round all numerical values to three decimal places.)V(t)(b) Do you believe that the equation in part (a) is a good fit?OThe model does not appear to be a good fit.OThe model appears to be a good fit.OThis cannot be determined.(c) The per capita consumption in 2001 had not yet been tabulated when the data in the table were published. What does the quadratic model give as the per capita consumption in 2001? (Round your answer to one decimal place.)190X pounds per person(d) According to your model, in what year will consumption exceed 225 pounds per person

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The per capita consumption of commercially produced fresh vegetables in a certain country from 1980 through 2000 was as shown in the accompanying table.
Per capita consumption of fresh vegetables
in a certain country
Vegetable consumption, V
(pounds per person)
Year
1980
147.1
1985
157
1990
167.1
1995
176.1
200.7
2000
(a) Find the function of the quadratic model that gives the per capita consumption of fresh vegetables in pounds per person, where t is the number of years since 1980, with data from 0 sts 20. Examine the equation graphed on a scatter plot of the data
(Round all numerical values to three decimal places.)
V(t)
(b) Do you believe that the equation in part (a) is a good fit?
OThe model does not appear to be a good fit.
OThe model appears to be a good fit.
OThis cannot be determined.
(c) The per capita consumption in 2001 had not yet been tabulated when the data in the table were published. What does the quadratic model give as the per capita consumption in 2001? (Round your answer to one decimal place.)
190
X pounds per person
(d) According to your model, in what year will consumption exceed 225 pounds per person
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The per capita consumption of commercially produced fresh vegetables in a certain country from 1980 through 2000 was as shown in the accompanying table. Per capita consumption of fresh vegetables in a certain country Vegetable consumption, V (pounds per person) Year 1980 147.1 1985 157 1990 167.1 1995 176.1 200.7 2000 (a) Find the function of the quadratic model that gives the per capita consumption of fresh vegetables in pounds per person, where t is the number of years since 1980, with data from 0 sts 20. Examine the equation graphed on a scatter plot of the data (Round all numerical values to three decimal places.) V(t) (b) Do you believe that the equation in part (a) is a good fit? OThe model does not appear to be a good fit. OThe model appears to be a good fit. OThis cannot be determined. (c) The per capita consumption in 2001 had not yet been tabulated when the data in the table were published. What does the quadratic model give as the per capita consumption in 2001? (Round your answer to one decimal place.) 190 X pounds per person (d) According to your model, in what year will consumption exceed 225 pounds per person

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Step 1

Part (a)

By the online regression calculator for the given data, the quadratic model for
the per capita consumption of fresh vegetables in pounds per person since 1980
is y 0.0801x2 +0.909x + 148.38 (approximating up to three digits)
0
147.1
5
157
10
167.1
15
176.1
200.7
20
V(x)
250
200
y-0.0809x+0.9089x+ 148.38
150
100
50
5
10
15
20
25
So, V(t) 0.081t2 0.909t +148.38 wheret is the number of years since
1980, with data from 0 < t < 20
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By the online regression calculator for the given data, the quadratic model for the per capita consumption of fresh vegetables in pounds per person since 1980 is y 0.0801x2 +0.909x + 148.38 (approximating up to three digits) 0 147.1 5 157 10 167.1 15 176.1 200.7 20 V(x) 250 200 y-0.0809x+0.9089x+ 148.38 150 100 50 5 10 15 20 25 So, V(t) 0.081t2 0.909t +148.38 wheret is the number of years since 1980, with data from 0 < t < 20

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Step 2

Part (b)

Yes, the model appears to be a good fit.                                   

 Part (c)

Per capita consumption of fresh vegetables in 2001.

So, t 2001 - 1980 = 21
.V(21) 0.081(21)2 0.909(21) 148.38 = 203.19 203.2
Therefore, the quadratic model gives 203.2 as per capita consumption in 2001
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So, t 2001 - 1980 = 21 .V(21) 0.081(21)2 0.909(21) 148.38 = 203.19 203.2 Therefore, the quadratic model gives 203.2 as per capita consumption in 2001

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Step 3

Part (d)...

V(t) 225
0.081t20.909t + 148.38
225
0.081t20.909t - 76.62 = 0
81t2909t-76620 = 0
Applying quadratic formula, we get
-909+/9092-4x81x(-76620)
t =
2x81
-909tv25651161
162
-909+25651161
o
-909-25651161
Either t
r t =
162
162
t 25.65 ort =-36.81
Since, t cannot be negative so t
26
26 1980 2006
Therefore, year =
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V(t) 225 0.081t20.909t + 148.38 225 0.081t20.909t - 76.62 = 0 81t2909t-76620 = 0 Applying quadratic formula, we get -909+/9092-4x81x(-76620) t = 2x81 -909tv25651161 162 -909+25651161 o -909-25651161 Either t r t = 162 162 t 25.65 ort =-36.81 Since, t cannot be negative so t 26 26 1980 2006 Therefore, year =

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