When Pinocchio tells a lie his nose grows about 30% of its original size you compare data about the number of lies he tells to the size of his nose. Which model is the best fit

Question

Linear
Quadratic
Exponential

Answer 1

To determine the best fitting model for the relationship between the number of lies Pinocchio tells and the size of his nose, we should consider how the nose grows with respect to the number of lies.

1. Linear: A linear model suggests that the size of the nose increases by a constant amount with each lie. However, since the nose grows by a percentage each time he lies, this model would not accurately represent the growth.

2. Quadratic: A quadratic model involves a squared term, suggesting that the size increases at a rate that changes (accelerates) with each additional lie. While this could represent some kinds of growth, it does not specifically fit the scenario of consistent percentage increases.

3. Exponential: An exponential model suggests that the size of the nose increases by a constant factor (e.g., 30% larger) with each lie. This means if he tells one lie, the size increases by 30%, and if he tells another lie, it increases by another 30% of the new size, resulting in compound growth.

Given that Pinocchio's nose grows by a percentage of its current size with each lie, the best model to describe this relationship is exponential growth.