Math Problem Statement
Lisa plants an oak tree in her back yard. She records the height of the tree each month.
Months Height (in.) 3 24.75 7 29.75 9 32.25 12 36
Choose the correct words to complete the statements.
Lisa’s tree is 5 in. when she first plants it, and it grows (Select) each month. In 2.5 years, the tree will be 90 in. tall. Time Remaining: 00:11:25© 2025 Renaissance Learning, Inc. All Rights Reserved.
Solution
Let's break down the information provided:
- Initially, the tree is 5 inches tall when Lisa first plants it.
- The tree's growth pattern is consistent each month.
From the table, we can see the tree grows as follows:
- After 3 months, the height is 24.75 inches.
- After 7 months, the height is 29.75 inches.
- After 9 months, the height is 32.25 inches.
- After 12 months, the height is 36 inches.
Growth per month:
- The tree grows by inches in 4 months (from 3 months to 7 months).
- This implies that the tree grows 5 inches in 4 months, which gives a growth rate of inches per month.
Thus, the correct completion for the statement is:
"Lisa’s tree is 5 inches when she first plants it, and it grows 1.25 inches each month."
In 2.5 years (30 months), the tree will be:
- The initial height is 5 inches.
- The tree grows 1.25 inches per month for 30 months.
- Total growth = inches.
So, in 2.5 years, the tree will be:
- inches tall.
But you are asked for the tree to be 90 inches tall, which suggests the tree's growth rate or the starting height might need a reevaluation, or that there is missing data or an issue with the wording.
Let me know if you have any questions or if you’d like further clarifications!
Here are some follow-up questions to deepen the understanding of tree growth rates:
- How would the tree's height change if the growth rate increased to 1.5 inches per month?
- What is the formula for calculating the height of the tree at any given month?
- How do seasonal variations affect the growth rate of trees like oak trees?
- Can you model the tree’s height with a linear equation?
- How would the tree’s height change if it initially started at a height of 10 inches?
Tip: When working with rates of growth like this, always make sure to calculate the rate of change first (like we did with the 1.25 inches per month), and then apply that rate to the given time frame for future predictions.
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Math Problem Analysis
Mathematical Concepts
Growth Rate
Linear Relationships
Unit Rate
Time-based Calculation
Formulas
Growth = Initial Height + (Growth Rate per Month * Time in Months)
Theorems
Linear Growth Model
Suitable Grade Level
Grades 6-8