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Exponential and logarithmic functions. Yr 11 maths methods. Objectives for Term 2. To define and understand exponential functions. To sketch graphs of the various types of exponential functions. To understand the rules for manipulating exponential and logarithmic expressions.

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## Exponential and logarithmic functions

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**Exponentialand logarithmicfunctions**Yr 11 maths methods**Objectives for Term 2**• To define and understand exponential functions. • To sketch graphs of the various types of exponential functions. • To understand the rules for manipulating exponential and logarithmic expressions. • To solve exponential equations. • To evaluate logarithmic expressions. • To solve equations using logarithmic methods. • To sketch graphs of functions of the form y = logax and simple transformations of this. • To understand and use a range of exponential models. • To sketch graphs of exponential functions. • To apply exponential functions to solving problems.**Introduction**• Functions in which the independent variable is an index number are called indicial or exponential functions. For example: • f (x) = ax where a > 0 and a ≠ 1 • quantities which increase or decrease by a constant percentage in a particular time can be modelled by an exponential function. • Exponential functions can be seen in everyday life for example in science and medicine (decay of radioactive material, or growth of bacteria like those shown in the photo), and finance ( compound interest and reducing balance loans).**Multiplication**• When multiplying two numbers in index form with the same base, add the indices. • For example, 23 × 24 =(2 × 2 × 2) × (2 × 2 × 2 × 2) = 27 am × an = am+ n**Division**• When dividing two numbers in index form with the same base, subtract the indices. am ÷ an = am- n**Raising to a power**• To raise an indicial expression to a power, multiply the indices. (am)n = am × n = amn**Raising to the power of zero**• Any number raised to the power of zero is equal to one. a0 = 1, a ≠ 0**Homework**• Page 220 Questions 1 – 3**Homework**• Page 220 – 221 - Questions 4 – 10

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