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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 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 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.

1 answer

To determine the type of functions that best model the success rates for Method A and Method B, we can analyze the data provided.

Method A

The values for Method A are:

  • Day 0: 1
  • Day 1: 3
  • Day 2: 5
  • Day 3: 7
  • Day 4: 9
  • Day 5: 11
  • Day 6: 13
  • Day 7: 15

The differences between consecutive days are constant:

  • (3-1) = 2
  • (5-3) = 2
  • (7-5) = 2
  • (9-7) = 2
  • (11-9) = 2
  • (13-11) = 2
  • (15-13) = 2

Since the differences are constant, this indicates that Method A can be modeled with a linear equation.

Method B

The values for Method B are:

  • Day 0: 7
  • Day 1: 3
  • Day 2: 1
  • Day 3: 1
  • Day 4: 3
  • Day 5: 7
  • Day 6: 13
  • Day 7: 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 themselves increase as we go further in the days, which suggests that the function has a more complicated relationship than linear — likely quadratic or possibly exponential. However, a closer analysis of the pattern leads to the interpretation that Method B is best modeled by a quadratic equation since its differences increase in a systematic fashion.

Based on this analysis, the correct response is:

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