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2 years ago

Number of Certified Organic Farms in the United States, 2001–2008

Mathematics

1 answer:

Vinil7 [7]2 years ago

6 0

Answer:

ŷ = 739.49X + 4876.43

y = 6755.98 - 388.24x + 125.30x²

y = 5428.98(1.09)^x

B.)

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

y = 12271.3

Year 2011 ; x = 11

y = 739.49(11) + 4876.43

y = 13010.8

Quadratic :

Year 2009 ; x = 9

y = 6755.98 - 388.24(9) + 125.30(9^2)

y = 13411.1

Year 2010 ; x = 10

y = 6755.98 - 388.24(10) + 125.30(10^2)

y = 15403.6

Year 2011 ; x = 11

y = 6755.98 - 388.24(11) + 125.30(11^2)

y = 17646.6

Exponential:

Year 2009 ; x = 9

y = 5428.98(1.09)^9

y = 11791.2

Year 2010 ; x = 10

y = 5428.98(1.09)^10

y = 12852.4

Year 2011 ; x = 11

y = 5428.98(1.09)^11

y = 14009.1

Step-by-step explanation:

X :

6231

6574

7237

7211

7701

8581

10302

11796

Using the online linear regression calculator :

The linear trend :

ŷ = 739.49X + 4876.43

Where x = year

With 2006 representing 1 ; and so on

Slope = m = 739.49

Intercept (c) = 4876.43

y = predicted variable

The quadratic model:

General form:

y = A + Bx + Cx²

y = 6755.98 - 388.24x + 125.30x²

The exponential model:

y = AB^x

y = 5428.98(1.09)^x

B.) Next three years :

Year 2009 ; x = 9

Year 2010 ; x = 10

Year 2011 ; x = 11

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

y = 12271.3

Year 2011 ; x = 11

y = 739.49(11) + 4876.43

y = 13010.8

Quadratic :

Year 2009 ; x = 9

y = 6755.98 - 388.24(9) + 125.30(9^2)

y = 13411.1

Year 2010 ; x = 10

y = 6755.98 - 388.24(10) + 125.30(10^2)

y = 15403.6

Year 2011 ; x = 11

y = 6755.98 - 388.24(11) + 125.30(11^2)

y = 17646.6

Exponential:

Year 2009 ; x = 9

y = 5428.98(1.09)^9

y = 11791.2

Year 2010 ; x = 10

y = 5428.98(1.09)^10

y = 12852.4

Year 2011 ; x = 11

y = 5428.98(1.09)^11

y = 14009.1

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Step-by-step explanation:

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Step-by-step explanation:

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