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Sagot :
Data:
x: number of months
y: tree's height
Tipical grow: 0.22
Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)
In this case the slope (m) or rate of change is the tipical grow.
m=0.22
To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):
[tex]\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}[/tex]Use the slope(m) and y-intercept (b) to write the equation:
[tex]\begin{gathered} y=mx+b \\ \\ y=0.22x+17.2 \end{gathered}[/tex]A) This line's slope-intercept equation is: y=0.22x+17.2B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:
[tex]\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\ \\ y=23.58 \end{gathered}[/tex]Then, after 29 months the tree would be 23.58 feet in heightC) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:
[tex]\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\ \\ 58=x \end{gathered}[/tex]Then, after 58 months the tree would be 29.96feet tall
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