Ask a New Question
Menu

Use the table to answer the question.

Day 0 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7
Method A 1 3 5 7 9 11 13 15
Method B 7 3 1 1 3 7 13 21
The table displays success rates for two different techniques used to memorize multiplication facts. The table shows how many multiplication facts a child memorized after the given number of days using either Method A or Method B. What type of function should be used to model each method?

(1 point)
Responses

Method A should be modeled with a linear equation, and Method B should be modeled with an exponential equation.
Method A should be modeled with a linear equation, and Method B should be modeled with an exponential equation.

Method A should be modeled with a quadratic equation, and Method B should be modeled with a quadratic equation.
Method A should be modeled with a quadratic equation, and Method B should be modeled with a quadratic equation.

Method A should be modeled with a linear equation, and Method B should be modeled with a quadratic equation.
Method A should be modeled with a linear equation, and Method B should be modeled with a quadratic equation.

Method A should be modeled with an exponential equation, and Method B should be modeled with a linear equation.
Method A should be modeled with an exponential equation, and Method B should be modeled with a linear equation.

1 answer

To analyze the success rates from the table for both Method A and Method B, we can observe the patterns in the data.

  • Method A:

    • The values increase by a constant amount each day:
      • From Day 0 to Day 1: \(3 - 1 = 2\)
      • From Day 1 to Day 2: \(5 - 3 = 2\)
      • This pattern continues, as the increase is consistently \(2\).
    • Thus, Method A can be modeled by a linear equation, as it follows a straight line pattern defined by \(y = mx + b\).

  • Method B:

    • The values do not increase consistently; they fluctuate:
      • From Day 0 to Day 1: \(3 - 7 = -4\)
      • From Day 1 to Day 2: \(1 - 3 = -2\)
      • From Day 2 to Day 3: \(1 - 1 = 0\)
      • From Day 3 to Day 4: \(3 - 1 = 2\)
      • The changes vary, which suggests a more complex relationship indicating non-linear growth.
    • Observing further, there is not a consistent pattern in the increase, which suggests that it might be modeled with a quadratic equation.

Based on this analysis, the correct answer would be:

Method A should be modeled with a linear equation, and Method B should be modeled with a quadratic equation.