How JustAnswer Works:
  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site.
    Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.
Ask Martin Your Own Question
Martin, Physicist
Category: Pre-Calculus
Satisfied Customers: 781
Experience:  20+ years of research, engineering and teaching
Type Your Pre-Calculus Question Here...
Martin is online now
A new question is answered every 9 seconds

Explain the concept of modeling. How does a model describe

This answer was rated:

Explain the concept of modeling. How does a model describe known data and predict future data? How do models break down? Can you think of an example?
Hello. I'll be right back with your answer...
Customer: replied 4 years ago.

The concept of modeling is the use of mathematics to predict the behavior of a system. It can be as simple as finding the trend in car prices, or as complex as modeling the climate of the Earth. In all cases, we describe the system by mathematical equations. The equation can be based on underlying physical principles, like gravity or electromagnetism, or they can be empirical models derived by fitting them to a set of observations. For example, we might measure the temperature at noon everyday. If we start in March, we might notice that after a month or so there is a gradual warming. We could fit a straight line to these data, and then we could predict the average temperature in June. This might work quite well, but the model wouldn’t be realistic for long-term prediction, since it would predict the temperatures keep rising. Come October, the temperatures will have stopped rising and begun cooling, and we would find our linear model isn’t adequate. After a year, we’d notice a cyclical pattern, and could then possibly fit a oscillatory function to the year-long temperatures, and come up with a good model.

The reason our initial linear model failed (in our hypothetical story) is because it extrapolated into uncharted territory. This is always a risky proposition. In general, when using empirical models like our temperature model, it’s a bad idea to extrapolate too far beyond the end of the observed data. Other ways that empirical models can break down is by spurious data. For example, suppose the thermometer was bumped or otherwise changed during the measurements, making the last few measurements colder than the actual temperature. This would skew the best-fit line, and our model would under-predict the future temperatures.

Martin and other Pre-Calculus Specialists are ready to help you
Just following up. It was a pleasure working with you. Please don't hesitate to let me know if you ever have additional questions. Just put "For Martin" at the beginning of your question, and I'll be sure to get it.


Related Pre-Calculus Questions