Math Problem Statement

According to the table, what was the rate of change between 2014 and 2018?

Solution

The question in the image asks to calculate the rate of change in the length of the annual school play between 2014 and 2018.

To calculate the rate of change, we use the following formula:

Rate of Change=Change in LengthChange in Year=LendLstartTendTstart\text{Rate of Change} = \frac{\text{Change in Length}}{\text{Change in Year}} = \frac{L_{\text{end}} - L_{\text{start}}}{T_{\text{end}} - T_{\text{start}}}

Where:

  • Lend=82L_{\text{end}} = 82 (length in 2018)
  • Lstart=82L_{\text{start}} = 82 (length in 2014)
  • Tend=2018T_{\text{end}} = 2018
  • Tstart=2014T_{\text{start}} = 2014

Let's calculate the rate of change:

Rate of Change=828220182014=04=0\text{Rate of Change} = \frac{82 - 82}{2018 - 2014} = \frac{0}{4} = 0

Thus, the rate of change between 2014 and 2018 is 0 minutes per year.

Would you like any more details or have any questions?

Here are 5 related questions for you:

  1. How do you calculate the rate of change when the values differ?
  2. What would the rate of change be between 2015 and 2018?
  3. Can the rate of change be negative, and if so, what does it represent?
  4. Why is it important to calculate the rate of change in real-world situations?
  5. What if the years were non-consecutive? How would that affect the calculation?

Tip: When calculating rate of change, always check if the values are increasing or decreasing to understand the direction of the change.

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Math Problem Analysis

Mathematical Concepts

Rate of Change
Algebra
Linear Functions

Formulas

Rate of Change = (L_end - L_start) / (T_end - T_start)

Theorems

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Suitable Grade Level

Grades 6-8