SOLUTION: To celebrate his birth, Damien's parents planted a tree in their yard. The tree's growth each year, in feet, can be modeled by the equation f(x)=2.5x+4. The tree is expected to re

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Question 1151304: To celebrate his birth, Damien's parents planted a tree in their yard. The tree's growth each year, in feet, can be modeled by the equation f(x)=2.5x+4. The tree is expected to reach full height when Damien is 18 years old. Interpret the values in the function to answer the given questions.
What was the height of the tree in feet when it was planted?
How tall will with tree be in feet when Damien is 18 years old?
What is the domain for the function?
What is the range for the function?
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The tree's growth each year, in feet, can be modeled by the equation:

f%28x%29=2.5x%2B4 where x represents the number of years, and 4 represents the height of the tree in feet when it was planted
when Damien is 18 years old means x=18, and
f%28x%29=2.5%2A18%2B4
f%28x%29=45%2B4
f%28x%29=49 =>tree will be 49 feet tall

domain:
R (all real numbers)
range:
R (all real numbers)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Problem

To celebrate his birth, Damien's parents planted a tree in their yard. The tree's growth each year, in feet, can be modeled by the equation f(x)=2.5x+4. The tree is expected to reach full height when Damien is 18 years old. Interpret the values in the function to answer the given questions.

What was the height of the tree in feet when it was planted?
Answer: 4 feet

To get this answer, plug in x = 0.
f(x) = 2.5*x + 4
f(0) = 2.5*0 + 4
f(0) = 0 + 4
f(0) = 4
The input x = 0 leads to y = f(x) = 4.
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How tall will with tree be in feet when Damien is 18 years old?

Answer: 49 feet

Now plug in x = 18
f(x) = 2.5*x + 4
f(18) = 2.5*18 + 4
f(18) = 45 + 4
f(18) = 49
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What is the domain for the function?

The domain is the set of real numbers x such that 0+%3C=+x+%3C=+18. Which can be described as "the set of numbers between 0 and 18 inclusive of both endpoints". We stop at x = 18 because the tree reaches its full height at this point. We have x = 0 as the lower boundary because negative year values do not make sense.

The domain in interval notation is [0, 18]. The square brackets tell the reader "include the endpoints".
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What is the range for the function?

The range is a similar story: The range is 0+%3C=+y+%3C=+49 which in interval notation would be [0, 49]. The smallest the tree can get is 0 ft, and the largest it can be is 49 feet.