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A scientist is studying red maple tree growth in a state park. She measured the trunk diameters of a sample of trees in the same month every other year. The tables show the data for two of the trees. This is the final year in which she will collect data. When her data collection is complete, she will predict future red maple tree growth. In year 13, the scientist will put tree wrap around tree 1 to protect it from the winter snow. The height of the tree wrap needs to be 45 inches. The wrap is priced by the square foot. To the nearest square foot, how many square feet of wrap does she need? A. 22 B. 44 C. 121 D. 261

Respuesta :

NetherFury

Answer:

(A) 22

Step-by-step explanation:


MrRoyal

The data for tree 1 is an illustration of a linear equation.

The scientist needs 22 square feet of wrap

From the complete question, we have the following points

[tex]\mathbf{(x_1,y_1) = (1,18.6)}[/tex]

[tex]\mathbf{(x_2,y_2) = (3,19.2)}[/tex]

First, we calculate the slope (m)

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{19.2 - 18.6}{3 -1}}[/tex]

[tex]\mathbf{m = \frac{0.6}{2}}[/tex]

[tex]\mathbf{m = 0.3}[/tex]

The equation is then calculated as:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{y = 0.3(x - 1) + 18.6}[/tex]

[tex]\mathbf{y = 0.3x - 0.3+ 18.6}[/tex]

[tex]\mathbf{y = 0.3x + 18.3}[/tex]

In year 13, the value of x is 13.

So, we have:

[tex]\mathbf{y =0.3 \times 13 + 18.3}[/tex]

[tex]\mathbf{y =22.2}[/tex]

Approximate

[tex]\mathbf{y =22}[/tex]

Hence, the scientist needs 22 square feet of wrap

Read more about linear equations at:

https://brainly.com/question/21088228

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