Answer:
The tree was 40 inches tall when planted
The tree's growth rate is 10 inches per year
Ten years after planting, is 140 inches tall
Step-by-step explanation:
From the graph attached, the height of the tree is plotted on the y axis and the year is on the x axis. The line passes through (2, 60) and (5, 90). The equation of a line passing through two point is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Therefore the equation of the line passing through (2, 60) and (5, 90) is:
[tex]y-60=\frac{90-60}{5-2}(x-2) \\y-60=\frac{30}{3} (x-2)\\y-60=10(x-2)\\y-60=10x-20\\y=10x-20+60\\y=10x+40[/tex]
The equation of a line in standard form is y = mx + c where c is the intercept on y axis and m is the slope. Since y = 10x + 40, m = 10 and c = 40.
The y intercept is 40 inches, this means the height of the tree at 0 years was 40 inches tall when planted, therefore The tree was 40 inches tall when planted is correct.
The slope of the line is 10, this means the tree grow at a rate of 10 inches per year. Therefore The tree's growth rate is 10 inches per year is correct.
The tree was 2 years old when planted is not correct
The slope of a linear function is constant, therefore the growth rate is constant. As it ages, the trees growth rate slows is not correct
The height of the tree at 10 years can be gotten by substituting x = 10 in y = 10x + 40. y = 10(10) + 40 = 100 + 40 = 140 inches. Therefore Ten years after planting, it is 140 inches tall. is correct
