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

1 answer

To determine the type of function suitable for modeling each method based on the data provided in the table, we can analyze how the multiplication facts memorized change over the days.

Method A:

  • The values in Method A are: 1, 3, 5, 7, 9, 11, 13, 15.
  • The differences between successive days are constant:
    • 3 - 1 = 2
    • 5 - 3 = 2
    • 7 - 5 = 2
    • ...

This indicates a linear relationship because the change (or rate of change) is constant.

Method B:

  • The values in Method B are: 7, 3, 1, 1, 3, 7, 13, 21.
  • The changes between successive days are not consistent:
    • 3 - 7 = -4
    • 1 - 3 = -2
    • 1 - 1 = 0
    • 3 - 1 = 2
    • 7 - 3 = 4
    • 13 - 7 = 6
    • 21 - 13 = 8

The rate of change is increasing, which might suggest a quadratic pattern since the second differences are consistent.

Based on this analysis:

  • Method A is best modeled by a linear equation because it shows a constant rate of increase.
  • Method B shows a varying rate of increase that suggests a quadratic equation due to the increasing differences.

Given this, the correct answer is:

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