Using Log Graphs in Modelling What are log graphs? Log graphs are used when the scale of a graph increases or decreases exponentially It can very difficult to read specific values from graphs with ...
Using Exps & Logs in Modelling What is exponential modelling? Exponential modelling is where real-life situations are modelled using exponential growth and decay Exponential growth is typically...
Exponential Growth & Decay What are exponential growth and exponential decay? y = Aekt is exponential growth y = Ae-kt is exponential decay k > 0 so plus or minus sign in equation immediatel...
Exponential Equations What are exponential equations? An equation where the unknown is a power In simple cases the solutions can be “spotted” How do I solve exponential equations? Laws of Indices a...
Laws of Logarithms What are the laws of logarithms? Two of these were seen in the notes Logarithmic Functions Beware … … log (x + y) ≠ log x + log y Results apply to ln too How do I use the laws of...
Derivatives of Exponential Functions What is the derivative of e? y = ex has the particular property ie for every real number x, the gradient of y = ex is also equal to ex (see Derivatives of Expon...
"e" Exponential Function What is e, the exponential function? The exponential function is y = ex e is an irrational number e ≈ 2.718 As with other exponential graphs y = ex passes through (0, 1) ha...
Logarithmic Functions Logarithmic functions a = bx and log b a = x are equivalent statements a > 0 b is called the base Every time you write a logarithm statement say to yourself what it means l...
Exponential Functions Exponential functions Exponential functions of the form y = ax with a > 0 are considered at A level Exponential graphs All graphs of the form y = ax will pass through (0, 1...
