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Euler's Number:
An irrational number that is also the natural logarithm base, e, where e ≈ 2.71828182845.
It is also the only number where the derivative of the exponential is equivalent to the original function. In other words, d(e^x)/dx = e^x.
Exponential Function:
An exponential function exists in the form f(x) = k*b^(a*x), where k is the pronumeral, b is the base being impacted by a*x which are the exponents. x is dependent on the position on the x-axis. This function also has an asymptote where the function approaches but never reaches.
Gradient Function:
This is the first derivative of a given function. When substituting a particular point into this first derivative, the gradient of the initial function at that point can be determined.
Index Laws:
Also known as the Law of Indices, Index Laws define ways that expressions involving indices can be simplified or expanded. Where indices are the numbers appearing on the top right of another number.
Inverse relationship:
A relationship involving two values where one is increasing whilst the other is decreasing.
Log Base:
The log base is the value 'a' as seen in the image to the right. It is the name of this component of a logarithmic function and can be rearranged into expontential form.
Logarithm:
"the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, y is the logarithm of x to the base a if ay = n, in which case one writes y = loga x."
Refer to image for 'Log Base' definition for visual.
Logarithmic Laws:
These are laws that can be used to simplify or expand logarithmic functions. These laws are depicted in the image to the right.
Logarithmic Scale:
A way to represent data that has a very large spread. The difference between each value on this scale is not linear, and is instead a magnitude different to the value either side of it. See image on the right for an example and comparison to a linear scale.
Model:
A mathematical representation of real-life situations. These models can then be used to find out more information about these real-life situations, such as using trend lines to make mathematically justified predictions.
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