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Answer:
- <u><em>The height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.</em></u>
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Explanation:
Please, find attached an image with the table that accompanies this question.
<u>1. Pattern</u>
The table is:
Years: 2 4 5 8 9
Height (in.): 34 50 58 82 90
The most simple pattern is a linear pattern. A linear pattern has a constante rate of change.
The rate of change between two points is:
- rate of change = change in the output / changee in the input
Find the rate of change for the data:
- (50 - 34) in / (4 - 2) year = 16in / 2year = 8in/year
- (58 - 50) in / (5 - 4) year = 8in/1year = 8 in/year
- (82 - 58) in / (8 - 5) year = 24in / 3year = 8 in/year
- (90 - 82) in / (9 - 8) year = 8in / 1 year = 8 in/year
Hence, the heigth and the years since the tree was transplantated show a linear relationship: every year the tree grew 8 inches.
<u>2. Intial height:</u>
You can find the initial height of the tree by using the rate of change of the height.
- At year 2: height = 34 inches
- At year 1: height = 34 inches - 8 inches = 26 inches
- At year 0: height = 26 inches - 8 inches = 18 inches
<u>3. Relationship</u>
You can <em>describe the relationship</em> in terms of the initial height and the numbers of years since the tree was transplantated.
Then, the height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.
You can even write an equation (function):
- name H the height of the tree in inches
- name y the number of years since the tree was transplantated
- the equation is: H = 18 + y
