Respuesta :
Answer:
h = 2t + 4
Step-by-step explanation:
Solution:-
- The height of the tree = h
- The number of years elapsed after 2006 = t
- height h1 = 10 ft, t1 = ( 2009 - 2006 ) = 3 yrs
- height h2 = 16 ft, t2 = ( 2012 - 2006 ) = 6 years
- The linear model of tree height "h" as a function of time "t" years after 2006 can be expressed in the form:
h = m*t + c
Where, m = The rate of change of height
c = The initial height of tree in 2006.
- We will use the given data to evaluate constant "m".
Rate = m = ( h2 - h1 ) / ( t2 - t1)
m = ( 16 - 10 ) / ( 6 - 3 )
m = 6 / 3 = 2
- Then use "m" and given set of data to evaluate the initial height of tree "c" in year 2006.
h = 2*t + c
h1 = 2*t1 + c
c = 10 - 2*3 = 4 ft
- The linear model for the height of tree "h" as fucntion of time "t" years after 2006 will be:
h = 2t + 4
Answer:
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.
[TeX]m=\frac{h_{2}-h_{1}}{t_{2}-t_{1}}[/TeX]
[TeX]m=\frac{16-10}{3-0}[/TeX]
[TeX]m=\frac{6}{3}=2[/TeX]
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
