Concept 3

Use a model to make predictions and evaluate whether results are reasonable.

Substitute carefully, keep the units attached, and check whether the result is realistic.

Core Idea

To use a model well, substitute carefully, keep the units attached, and ask whether the output is realistic for the situation.

Understanding

Rule: Substitute carefully, then check whether the answer makes sense.

  • Put the input into the model and compute the output.
  • Attach the correct unit to the result.
  • Reject values that are negative, non-integer when a count is expected, or far outside the data range.

Step by Step

  1. Substitute the given input value into the model.
  2. Simplify and compute the output.
  3. Attach the correct unit to the result.
  4. Check that the size and sign of the answer make sense in the context.

Misconceptions

  • Substituting the wrong quantity into the model because the variables were not identified first.
  • Accepting a negative or impossible value without checking whether it makes sense in the situation.
  • Forgetting that a model based on data may be less reliable far outside the observed range.
Question

Worked Example

A school models the number of tickets sold for a show by 𝑇 =1800 −75𝑝, where 𝑝 is the ticket price in dollars. According to the model, how many tickets are predicted to sell when 𝑝 =12?

Select an answer to see the explanation