Question

Decide which, if any, of the models are appropriate for the given situations.

(2 points)
Responses

Predicting height, in inches, of children under 12. // Model: h = a² + 30
Predicting height, in inches, of children under 12. // Model: h = a² + 30

Predicting cost with fixed and hourly rates. // Model: C = 50 + 25h
Predicting cost with fixed and hourly rates. // Model: C = 50 + 25h

Predicting shoe size of elderly adults, based on age. // Model: s = a ÷ 3 - 20
Predicting shoe size of elderly adults, based on age. // Model: s = a ÷ 3 - 20

None of the situations have an appropriate model

Answer 1

Let's analyze each model based on the provided situations:

1. **Predicting height, in inches, of children under 12. // Model: h = a² + 30**
- This model, which includes a squared term (a²), is not appropriate for predicting height since height is generally a linear function of age (a) in this context. Moreover, it can lead to unrealistic height values as children's ages increase. **Not appropriate.**

2. **Predicting cost with fixed and hourly rates. // Model: C = 50 + 25h**
- This model is appropriate, as it represents a linear relationship where C represents total cost, 50 is the fixed rate, and 25h represents the variable cost based on hours worked (h). **Appropriate.**

3. **Predicting shoe size of elderly adults, based on age. // Model: s = a ÷ 3 - 20**
- This model suggests a linear relation where the shoe size decreases as age increases (since a is divided and decreased by 20). However, it may produce unrealistic shoe sizes for elderly adults, as it may not account for the fact that shoe sizes don't directly correlate to age in a straightforward way. **Not clearly appropriate; potentially unrealistic outputs.**

Based on this analysis, the only appropriate model is for the cost with fixed and hourly rates.

**Final Decision:**
**Only the second model is appropriate (Predicting cost with fixed and hourly rates: C = 50 + 25h).**