Expert: Paul Klarreich - 2/12/2008

Question
Suppose w = f(x) is the average daily quantity of water required by a tree of height x feet.

1. Suppose an average oak tree is a given area has a height of y. What does f(y + 10) represent?

--> I got confused when it came to this question on my homework. Since f(x) = w, then f(y + 10 more) = w? Please clarify this... Thank you!

Answer
Questioner:   Elaine
Category:  Calculus
Private:  No
 
Subject:  Integration
Question:  Suppose w = f(x) is the average daily quantity of water required by a tree of height x feet.

1. Suppose an average oak tree is a given area has a height of y. What does f(y + 10) represent?

>> You meant "in a given area", didn't you?

--> I got confused when it came to this question on my homework. Since f(x) = w, then f(y + 10 more) = w? Please clarify this... Thank you!
................................................
Hi, Elaine,

Applied math is about shorthand.  For example,  f(x) in your example is a shorthand for:  
 
The average daily quantity of water required by a tree of height (x)

So you can get a better understanding, we could un-shorthand the statements, and write your question of :

What does f(y + 10) represent?

as:

The average daily quantity of water required by a tree of height(y + 10) represent"

OOps -- that's it right there.

Now y+10 is a height, of course, and you have another shorthand:

an average oak tree in a given area has a height of y.  In other words,

y = the height of an average oak tree in a given area. so

y + 10 = the height of an average oak tree in a given area + 10

and:

f(y + 10) =

The average daily quantity of water required by a tree of height(y + 10)

which means

The average daily quantity of water required by a tree of height(the height of an average oak tree in a given area + 10)

which you can 'clean up' a bit, to say:

The average daily quantity of water required by a tree which is 10 feet higher than an average oak tree in a given area.