Math Problem Statement
A weeping willow that is 15 feet in height grows to a maximum height of 35 feet in y years at a constant rate of 24 inches per year. Which of the following equations best describes this situation?
Solution
To analyze this problem:
- The initial height of the weeping willow is 15 feet.
- The willow grows at a constant rate of 24 inches per year.
- The maximum height of the willow is 35 feet.
- We need to express this growth in terms of an equation and convert the growth rate from inches to feet.
Step-by-Step Solution
-
Convert the growth rate from inches to feet:
-
Set up the equation:
- The height after years would be the initial height plus the growth over years.
- Therefore, .
-
Determine when the height reaches 35 feet:
- Since we are looking for the point when the willow reaches 35 feet, we set .
- This gives us the equation:
Conclusion
The equation that best describes this situation is:
Answer: Option A, .
Would you like more details or have any questions?
Here are some additional questions related to this problem:
- How would the equation change if the growth rate was given in feet per year instead?
- What if the willow reached a different maximum height, say 40 feet? How would that impact the equation?
- How would we solve for if asked to find the number of years it takes to reach a height of 35 feet?
- What if the initial height was different, say 10 feet? What would the new equation look like?
- How could we represent this scenario graphically?
Tip: Converting units carefully is crucial in mixed-unit problems to ensure accuracy in equations and solutions.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Unit Conversion
Formulas
H = initial height + (growth rate * years)
Theorems
Linear Growth
Suitable Grade Level
Grade 8