3. Functions and Relations

Modeling With Functions — Quiz

Test your understanding of modeling with functions with 5 practice questions.

Practice Questions

Question 1

A linear model is created to predict the number of sales ($S$) of a product based on the advertising budget ($A$) in thousands of dollars. The model is given by $S = 50A + 1000$. If the company increases its advertising budget by $10$ thousand dollars, what is the predicted increase in sales?

Question 2

When creating a linear model from data, what is the most critical factor to consider when determining if a linear model is appropriate for the given data set?

Question 3

A linear model is used to predict the height ($H$) of a tree in feet based on its age ($A$) in years. The model is $H = 3.5A + 10$. If a tree is $15$ years old, what is its predicted height?

Question 4

A company's monthly expenses ($E$) in dollars are modeled by the linear function $E = 500C + 2000$, where $C$ is the number of units produced. If the company's expenses for a month were $12000$ dollars, how many units were produced?

Question 5

When assessing the reasonableness of a prediction made by a linear model, especially when extrapolating significantly beyond the observed data range, which of the following is the most critical consideration?