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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 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.

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.
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1 answer

To analyze the two methods based on the data provided in the table, we first observe the success rates for each method over the days.

Method A:

  • The values are 1, 3, 5, 7, 9, 11, 13, 15.
  • The differences between consecutive days are constant (2 each day: 3-1=2, 5-3=2, etc.).
  • This indicates a linear relationship.

Method B:

  • The values are 7, 3, 1, 1, 3, 7, 13, 21.
  • The differences between consecutive days are not constant:
    • 3 - 7 = -4
    • 1 - 3 = -2
    • 1 - 1 = 0
    • 3 - 1 = 2
    • 7 - 3 = 4
    • 13 - 7 = 6
    • 21 - 13 = 8
  • The differences are not constant, and they appear to show increasing patterns, suggesting a quadratic relationship.

Based on this analysis:

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

Therefore, the correct response is:

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