SOLUTION: The yearly production of a 5 foot orange tree is 35 pounds of oranges. A 12 foot tree produces 54 pounds. What is the predicted production of an 18 foot tree? What is the predic

Question 661979: The yearly production of a 5 foot orange tree is 35 pounds of oranges. A 12 foot tree produces 54 pounds.
What is the predicted production of an 18 foot tree?
What is the predicted production of an 20 foot tree?
What is the predicted height ( in feet ) of a tree that produces 88 pounds of oranges?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the production, of an orange tree varies linearly with its height, ,
we can write the linear equation that describes it, knowing two (,) points.
"The yearly production of a 5 foot orange tree is 35 pounds of oranges," gives us point (,).
"A 12 foot tree produces 54 pounds," gives us point (,).

I can see 3 ways to get the answer.
The expected way to solve the problem depends on what you are studying in class.

CALCULATING SLOPE OF A LINE AND WRITING THE POINT-SLOPE FORM:
We can calculate the slope, of the line:
--> .
Then we can use that slope and the coordinates of one of the points to write the equation in point-slope form.

From the point-slope form, we can go to the slope-intercept form, which will help answer the first 2 questions:
-->-->-->-->-->
With a calculator, we can use the approximation
and get accurate enough results.
I'll stick with the fractions just in case you are expected to do that.
For the 18 foot tree, , so
-->-->=about=about (rounding)
I assume the expected answer is rounding to whole numbers.
For the 20 foot tree,
--> -->-->=about=about (rounding)
I assume the expected answer is rounding to whole numbers.
For the 88 pound production, , so
-->-->-->
Multiplying both sides times :
-->-->=about=about (rounding)
I assume the expected answer is rounding to whole numbers.

SETTING UP A SYSTEM OF EQUATIONS TO FIND SLOPE AND INTERCEPT:
WE can find an equation of the form
by substituting the coordinates for out 2 points and solving the system

Solving the system of equations leads to
=about (rounding)
and =about (rounding)
From that point on, the calculations are the same as done above.

USING A COMPUTER/CALCULATOR AS IF IT IS A STATISTICS PROBLEM
Using Excel functions in my computer, I can answer all 3 questions.
With A1=5, A2=12, B1=35, B2=54,
=FORECAST(18,B1:B2,A1:A2) gives me or or pounds of oranges for an 18 foot tree.
=FORECAST(20,B1:B2,A1:A2) gives me or or pounds of oranges for an 20 foot tree.
=FORECAST(88,A1:A2,B1:B2) gives me feet for the height of a tree that would produce 88 pounds of oranges in a year.
RELATED QUESTIONS
yearly production of a 4 foot orange tree is 34 pounds of oranges. A 15 foot tree... (answered by stanbon)

The yearly production of a 5 foot orange tree is 42 pounds of oranges. A 15 foot tree... (answered by stanbon)

The yearly production of a 4 foot orange tree is 26 pounds of oranges. A 15 foot tree... (answered by josgarithmetic)

The yearly production of a 4ft Orange tree is 20 pounds of oranges. A 17ft tree produces... (answered by josgarithmetic)

there is a direct variation between number of oranges squeezed and the weight of the... (answered by ankor@dixie-net.com)

The question is and it doesnt make sense to me. A orange tree at 7ft tall products... (answered by richwmiller,scott8148)

I am trying to figure out how to predict the height of an orange tree that produces 88... (answered by nyc_function)

A forester is estimating the amount of lumber contained in a tree. When she stands 35... (answered by Cromlix)

A tree casts a shadow of 12 feet. At the same time a 6-foot man casts a 3-foot... (answered by checkley79)