1 Mathematical Modeling and Quantitative Reasoning Online Quiz Questions

True or false: A mathematical model is a simplified representation of a real-world situation rather than the situation itself.

What mathematical modeling term names a restriction imposed by a real-world situation on the values a model may use?

True or false: If the tank model $V(t)=500-4t$ produces a negative value after 125 minutes, that negative value represents a physically possible amount of water in the tank.

For the tank model $V(t)=500-4t$, which quantity is the input, or independent variable?

Which assumptions support the model $V(t)=500-4t$ for a draining tank? Select all correct choices.

A map uses the scale $1\text{ inch}=20\text{ miles}$. What actual distance, in miles, is represented by 3 inches?

A streaming service charges $C(n)=12+3n$, where $n$ is the number of premium movies rented. Which domain is appropriate for $n$?

Which questions are appropriate when evaluating whether a mathematical model is useful? Select all correct choices.

A cyclist travels 18 miles in 1.5 hours. Determine the cyclist's average speed, include the appropriate unit, and explain what additional step would be needed if the result were required in kilometers per hour.

A population graph labels its vertical axis in thousands of people. What does a vertical value of 8 represent?

A runner's distance is recorded as a function of elapsed time. Which quantity is the dependent variable?

True or false: A useful modeling assumption should be possible to evaluate using observations or data.

A map uses the scale $1$ inch = $20$ miles. What real-world distance, in miles, does a $3$-inch distance represent?

A car-rental cost is modeled by $C=50+0.20m$, where $m$ is the number of miles driven. What cost does the model predict for $150$ miles?

In a model where $n$ is the number of premium movies rented, what kind of value must $n$ be?

Which assumption supports the model $V(t)=500-4t$ for a draining tank?

Why is the expression $500-4t$ dimensionally consistent when $t$ is measured in minutes and the rate is $4$ gallons per minute?

The model $V(t)=500-4t$ gives a negative value when $t>125$. What is the best interpretation of this result?