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
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
Page 220 Questions 1 3
Answer without using your Cauculators
Answer with your calculators
Page 220 221 - Questions 4 10
Homeworknegative and rational powersnegative powers
Indicial equationsIndicial equations
Solve the following
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