The yearly production of a 6 foot orange tree is 40 pounds of oranges. A 16 foot tree produces 65 pounds.?
Let H represent the height of an orange tree and p the number of pounds of oranges produced.
a). List the ordered pairs. (H.P)
What is the ordered pair for the first tree? (6,40)
What is the ordered pair for the second tree: (16,65)
B. Find the point-slope form of an equation of the line through the two ordered pairs.
p - 40 = 5/2 (h-6)
C. Use the equation from part b)to predict the number of pounds of oranges produced by an 18 foot tree; a 20 foot tree.
What is the predicted production of an 18 foot tree?
What is the predicted production of an 20 foot tree?
D. Use the question from part b) to predict the height of a tree which produces 88 pounds of oranges.
What is the predicted height (in feet) of a tree that produces 88 pounds of oranges?
To find the predicted production of an 18 foot tree and a 20 foot tree, we can substitute the values into the equation from part B, which is:
p - 40 = 5/2(h - 6)
Let's find the predicted production for an 18 foot tree first:
p - 40 = 5/2(18 - 6)
p - 40 = 5/2(12)
p - 40 = 30
p = 30 + 40
p = 70
Therefore, the predicted production of an 18 foot tree is 70 pounds.
Now, let's find the predicted production for a 20 foot tree:
p - 40 = 5/2(20 - 6)
p - 40 = 5/2(14)
p - 40 = 35
p = 35 + 40
p = 75
Therefore, the predicted production of a 20 foot tree is 75 pounds.
To find the predicted height of a tree that produces 88 pounds of oranges, we can rearrange the equation from part B and solve for h:
p - 40 = 5/2(h - 6)
5/2(h - 6) = p - 40
5(h - 6) = 2(p - 40)
5h - 30 = 2p - 80
5h = 2p - 50
h = (2p - 50)/5
Let's plug in p = 88 into the equation to find the predicted height:
h = (2(88) - 50)/5
h = (176 - 50)/5
h = 126/5
h = 25.2
Therefore, the predicted height of a tree that produces 88 pounds of oranges is 25.2 feet.
To find the predicted production of an 18 foot tree and a 20 foot tree, we can use the equation from part B:
p - 40 = (5/2)(h - 6)
C. Use the equation from part B to predict the number of pounds of oranges produced by an 18 foot tree; a 20 foot tree.
To find the predicted production of an 18 foot tree, substitute h = 18 into the equation:
p - 40 = (5/2)(18 - 6)
p - 40 = (5/2)(12)
p - 40 = 60/2
p - 40 = 30
p = 30 + 40
p = 70
Therefore, the predicted production of an 18 foot tree is 70 pounds.
To find the predicted production of a 20 foot tree, substitute h = 20 into the equation:
p - 40 = (5/2)(20 - 6)
p - 40 = (5/2)(14)
p - 40 = 70/2
p - 40 = 35
p = 35 + 40
p = 75
Therefore, the predicted production of a 20 foot tree is 75 pounds.
D. Use the equation from part B to predict the height of a tree which produces 88 pounds of oranges.
To find the predicted height of a tree that produces 88 pounds, we need to rearrange the equation to solve for h:
p - 40 = (5/2)(h - 6)
Multiply both sides by 2/5 to isolate (h - 6):
2/5(p - 40) = h - 6
Multiply both sides by 5/2:
p - 40 = 5/2(h - 6)
Distribute 5/2:
p - 40 = (5/2)h - 30
Rearrange the equation:
(5/2)h = p - 10
Now, isolate h by dividing both sides by 5/2:
h = (2/5)(p - 10)
Substitute p = 88 into the equation:
h = (2/5)(88 - 10)
h = (2/5)(78)
h = 31.2
Therefore, the predicted height of a tree that produces 88 pounds of oranges is 31.2 feet.