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? There are many laws or rules of indices, for example am?x an?= am+n (am)n?= amn There are equivalent laws of logarithms (for a > 0) There are ...
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...
Approximating Values What is the general binomial expansion? The?general?binomial?expansion, as given in the formula booklet, is If?n?∈???then the expansion is?finite?(see Binomial Expansion) Other...
General Binomial Expansion - Multiple What is the general binomial expansion? The?general?binomial?expansion, as given in the formula booklet, is If?n?∈???then the expansion is?finite?(see Binomial...
General Binomial Expansion - Subtleties What is the general binomial expansion? The binomial expansion applies for positive integers,?n?∈?? The?general?binomial?expansion?applies to other types of ...
General Binomial Expansion What is the general binomial expansion? The binomial expansion applies for positive integers,?n?∈?? The?general?binomial?expansion?applies to other types of powers too Th...
