Why hasn't everyone already died of a contagion? And, if vampires exist, shouldn't we all be sucking blood by now? Students model the exponential growth of a contagion and use logarithms and finite geometric series to determine the time needed for a disease to infect the entire population. They'll also informally prove that vampires can't be real.

There are a lot of conflicting stories about vampire behavior in pop culture, so before we can answer this question, let's first agree on some ground rules:

1. If you're bitten by a vampire, you become a vampire.

2. Vampires need to drink human blood.

3. Vampires need to feed once a week.

For the sake of argument, let's say there's a vampire out there who plays by these rules. What would that mean for the future of mankind?

How much should Nintendo charge for the Wii U? Students use linear functions to explore demand for the Wii U console and Nintendo's per-unit profit from each sale. They use those functions to create a quadratic model for Nintendo's total profit and determine the profit-maximizing price for the console.

Are solar panels worth the cost? Students set up and solve systems of linear equations to compare different electricity plans and determine when each option is the least expensive.

How do you increase the horsepower of a car engine? Students calculate the volumes of different car cylinders, and explore ways to make engine even more powerful by changing the dimensions of an engine's internal geometry.

How much should states spend on schools and police? Students analyze histograms and use mean and median to explore state spending habits. Then, they discuss how much they think states should be spending.

When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.

What's the best way to position a car's mirrors? Students use reflections and congruent angles to determine the best orientation for rear- and side-view mirrors, and learn how to correct those dangerous blind spots.

How has the urban population changed over time, and will we all eventually live in cities? Students use recursive rules along with linear and exponential models to explore how America's urban areas have been growing over the last 200 years.

Why do tires appear to spin backwards in some car commercials? Students apply unit rates and the formula for the circumference of a circle to determine what makes a spinning wheel sometimes look like it’s moving in the opposite direction of the car sitting on top of it.

Does the same sound always sound the same? Students come up with equations in several variables to explore the Doppler Effect, which explains how sound from a moving object gets distorted.

How much Tylenol can you safely take? Students use exponential functions and logarithms to explore the risks of acetaminophen toxicity, and discuss what they think drug manufacturers should do to make sure people use their products safely.

In which MLB ballpark is it hardest to hit a home run? Students find the roots and maxima of quadratic functions to model the trajectory of a potential home-run ball.

How has the pace of technology changed over time? Students explore timelines of important technological milestones, and calculate the time between major events using absolute value and operations on integers.

How has the iPod depreciated over time? Students compare linear and exponential decay, as well as explore how various products have depreciated and what might account for those differences.

Are coupons a good deal? Students use unit rates and percents to explore the math and psychology behind retail discounts.

Should you buy a camera lens with vibration reduction? Students interpret graphs and use right triangle trigonometry to explore the relationship between focal length, viewing angle, and blurriness.