We are given that the palm tree on the left is 10 years old and the palm tree on the right is 8 years old.
The man standing between them is 6 feet tall. Then, we can say that the height of the palm tree on the right is approximately the double of the man's height. We can write this as an equation by using y to represent the height of the palm tree.
y≈ 2(6) → y ≈ 12 ft
The palm tree on the left is just a little bit bigger than the palm tree on the right. We can then say that the height of the palm on the left is approximately 2.5 times bigger than the height of the man.
y≈ 2.5(6) → y ≈ 15 ft
Consider that we have two points (x,y), where x is the age of each palm tree and y is the height of the tree.
Right Palm Tree:& (8,12)
Left Palm Tree:& (10,15)
Let's plot these points on a coordinate plane.
Recall that the slope is the rate of change between two variables.
m = y_2-y_1/x_2-x_1
In our case, x represents the age of the palm tree and y the height of the tree. Let's substitute the points given on the graph of Part B, (8,12) and (10,15), into the above formula and calculate m.
We calculated that the slope is 1.5. Therefore, the rate of growth for the palm trees is 1.5 feet per year.
We want to write an equation that represents the height of a palm tree in terms of its age. To do so, recall the slope-intercept form of a linear equation.
y= mx+ b
In this form, m is the slope and b is the y-intercept. The y-intercept is the y-value where the line crosses the y-axis. It occurs when x=0. In our case, x represents the age and y the height of each palm tree. Since the growth of rate is 1.5 feet per year, the height of the palm tree in the initial year x=0 is 0. Then, the y-intercept is b= 0.
y= 1.5x+ 0 → y=1.5x
