Maths: Applications and Interpretation · Functions. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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A model is a function chosen to describe real data. An exponential model fits a quantity that is multiplied by the same factor in each equal step of time, such as a population or a cooling drink. Its graph flattens towards a horizontal asymptote. In a decay model this is the long-term value.
A sinusoidal model fits a quantity that repeats in a regular wave, such as tides or the height of a seat on a wheel. You describe it by its amplitude, its period and its principal axis.
To build a model, choose the type from the shape of the data, find the parameters, then test it. A model is only trusted inside the range of the data. Using it far outside that range is extrapolation and is risky.
Students give the starting value as the long-term value. In a decay model y = k × ax + c (0 < a < 1) the long-term value is c, the number added on, not k or k + c.
Answer: Period 24 hours; maximum temperature 24 °C.
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