A mathematical model is a description of a system using mathematical tools. For example, my work involves developing mathematical models of cancer. I write up algorithms that describe how the cancer grows and interacts with other cells within the body. We can then use this to find new treatment approaches as we can test a lot of situations quickly.
Fiona’s answer is really good.
I’d add that you probably use models every day without really thinking about it. Say you need to cook pasta for 10 people: 6 adults and 4 small kids. You might decide that each adult needs a handful of pasta, and each child needs only half a handful. This is a model – you could express it mathematically as (total pasta)= (number of adults) + 1/2(number of children).
After trying this, you might find that it isn’t quite working and that you need to adjust your amounts or collect additional information (do boys eat more than girls? do tall people eat more than short).
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