Question Choose a system of linear equations to represent the growth of a inch per year spruce tree and a inch per year hemlock tree with initial heights of inches and inches, respectively.
Studdy Solution
STEP 1
Assumptions
1. The spruce tree grows at a constant rate of 4 inches per year.
2. The hemlock tree grows at a constant rate of 6 inches per year.
3. The initial height of the spruce tree is 14 inches.
4. The initial height of the hemlock tree is 8 inches.
5. We are looking for a system of linear equations to represent the growth of these trees over time.
STEP 2
Define the variables for the system of linear equations.
Let represent the number of years after the trees have been planted.
Let represent the height of the trees in inches after years.
STEP 3
Write the linear equation for the spruce tree using its growth rate and initial height.
For the spruce tree, the height each year is the initial height plus the growth per year times the number of years, which gives us the equation:
STEP 4
Write the linear equation for the hemlock tree using its growth rate and initial height.
For the hemlock tree, the height each year is the initial height plus the growth per year times the number of years, which gives us the equation:
STEP 5
Combine the equations for both trees into a system of linear equations.
The system of linear equations that represents the situation is:
This system of equations can be used to determine the height of each tree after any given number of years, as well as to find out when both trees will be of the same height, if needed.
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