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:

  1. The initial height of the weeping willow is 15 feet.
  2. The willow grows at a constant rate of 24 inches per year.
  3. The maximum height of the willow is 35 feet.
  4. We need to express this growth in terms of an equation and convert the growth rate from inches to feet.

Step-by-Step Solution

  1. Convert the growth rate from inches to feet: 24 inches per year=2412 feet per year=2 feet per year24 \text{ inches per year} = \frac{24}{12} \text{ feet per year} = 2 \text{ feet per year}

  2. Set up the equation:

    • The height HH after yy years would be the initial height plus the growth over yy years.
    • Therefore, H=15+2yH = 15 + 2y.
  3. Determine when the height reaches 35 feet:

    • Since we are looking for the point when the willow reaches 35 feet, we set H=35H = 35.
    • This gives us the equation: 35=15+2y35 = 15 + 2y

Conclusion

The equation that best describes this situation is:

Answer: Option A, 35=15+2y35 = 15 + 2y.

Would you like more details or have any questions?


Here are some additional questions related to this problem:

  1. How would the equation change if the growth rate was given in feet per year instead?
  2. What if the willow reached a different maximum height, say 40 feet? How would that impact the equation?
  3. How would we solve for yy if asked to find the number of years it takes to reach a height of 35 feet?
  4. What if the initial height was different, say 10 feet? What would the new equation look like?
  5. 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