Exponential and logarithmic functions

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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. - PowerPoint PPT Presentation

Text of Exponential and logarithmic functions

Exponential and logarithmic functions

Exponentialand logarithmicfunctionsYr 11 maths methodsTo 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.

Objectives for Term 2

IntroductionFunctions 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 1quantities 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).

Index lawsMultiplicationam an = am + nWhen multiplying two numbers in index form with the same base, add the indices.For example, 23 24 = (2 2 2) (2 2 2 2) = 27Divisionam an = am - nWhen dividing two numbers in index form with the same base, subtract the indices.

Raising to a power(am)n = am n = amnTo raise an indicial expression to a power, multiply the indices.

Raising to the power of zeroa0 = 1, a 0Any number raised to the power of zero is equal to one.

Products and quotients

Remember

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Page 220 Questions 1 3

HomeworkMore Questions

Answer without using your Cauculators

Answer with your calculators

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Answer (b)

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Page 220 221 - Questions 4 10

Homeworknegative and rational powersnegative powers

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Answer B

Rational powers

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Examples

Indicial equationsIndicial equations

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Answer B

Answer C

Solve the following

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Answer

Graphs of exponential functionsGraphs of exponential functions

The effect of changing the a coeffThe effect of changing the a coeffThe effect of changing the a coeffReflections of exponential functions

Reflections of exponential functionsReflections of exponential functionsHorizontal translations of exponential functions

Vertical translations of exponentialfunctions

Dilation from the x-axis

Dilation from the y-axis

Examples

Examples

Calculator time.