In 2009, a tree was 10 feet tall. In 2012, the tree was 16 feet tall. Construct a linear model that represents the height, h, of the tree t years after 2006.

h(t)=2t+4

Step-by-step explanation:

In 2009, h(t=0)=10 feet

In 2012, h(t=3)=16 feet

Let us determine the rate of the growth of the tree.

The equation of the trees growth can be written as:

h(t)=2t+c

When h=16, t=3

Using these values to solve for c

16=2(3)+c

c=16-6=10

Therefore the equation of the tree's growth is:

h(t)=2t+10

To determine the linear model that represents the tree's growth after 2006, i.e. three years before 2009

We substitute t=t-3

h(t)=2(t-3)+10

=2t-6+10=2t+4

The linear model that represents the tree's growth t years after 2006 is:

h(t)=2t+4

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

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