Question

can you give a description of the relationship between the years since the tree was transplanted and its height in inches? if so what is it?

Answer 1

Answer:

• The height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.

Explanation:

Please, find attached an image with the table that accompanies this question.

1. Pattern

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.

2. Intial height:

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

3. Relationship

You can describe the relationship 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