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
Algebra.Com
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(20849) (Show Source): You can put this solution on YOUR website!
The tree's growth each year, in feet, can be modeled by the equation:
where represents the number of years, and represents the height of the tree in feet when it was planted
when Damien is years old means , and
=>tree will be feet tall
domain:
(all real numbers)
range:
(all real numbers)
Answer by jim_thompson5910(35256) (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.
--------------------------------------------
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
--------------------------------------------
What is the domain for the function?
The domain is the set of real numbers x such that . 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".
--------------------------------------------
What is the range for the function?
The range is a similar story: The range is 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.
RELATED QUESTIONS
a pine sapling was 3 meters tall when it was first planted. in its first year, it grew 1... (answered by greenestamps)
In a 225 meter long yard 26 tre
e
s are planted at equal distance, one tree being at... (answered by KMST)
A certain kind of tree increases in height by 25 percent each year. It was 2.5 feet tall... (answered by checkley77)
A tree house costs $530. You plan to save $10 each week. Your parents will help pay $80... (answered by tutor_paul)
A graphing calculator is recommended.
For a certain type of tree, the diameter D (in... (answered by Theo)
The height, h, of a particular tree in feet t years after transplanting can be found... (answered by josgarithmetic)
a small tree was planted at a height of 7 feet. the tree has been planted for 14 month,... (answered by stanbon)
dina planted an eight foot tree in her backyard which she expects to grow at a rate of 4... (answered by josmiceli)
Part A: A tree is planted on a farm. The tree was 5 feet tall when it was planted. The... (answered by solver91311)