Exponential and logarithmic functions
description
Transcript of Exponential and logarithmic functions
Exponentialand logarithmic
functionsYr 11 maths methods
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.
Objectives for Term 2
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).
Index laws
Multiplication
am × an = am + n 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
Division
am ÷ an = am - n When dividing two numbers in index form with the same base, subtract the indices.
Raising to a power
(am)n = am × n = amn To raise an indicial expression to a power, multiply the indices.
Raising to the power of zero
a0 = 1, a ≠ 0 Any number raised to the power of zero is equal to one.
Products and quotients
Remember
Questions
Answers (a)
Answers (b)
Answers (c)
Answers (d)
Page 220 Questions 1 – 3
Homework
More Questions
Answer without using your Cauculators
Answer with your calculators
Questions
Answer (a)
Answer (b)
Question
Answer
Page 220 – 221 - Questions 4 – 10
Homework
negative and rational powers
negative powers
Examples
Answer A
Answer B
Rational powers
Examples
Examples
Indicial equations
Indicial equations
Examples
Answer A
Answer B
Answer C
Solve the following
Answer
Answer
Graphs of exponential functions
Graphs of exponential functions
The effect of changing the “a” coeff
-4 -3 -2 -1 0 1 2 3 40
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y=2^x y=3^x y=2^-x y=3^-x
The effect of changing the “a” coeff
-4 -3 -2 -1 0 1 2 3 40
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y=2^xy=3^x
The effect of changing the “a” coeff
-4 -3 -2 -1 0 1 2 3 40
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y=2^-xy=3^-x
Reflections of exponential functions
Reflections of exponential functions
-4 -3 -2 -1 0 1 2 3 40
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y=2^xy=2^-x
Reflections of exponential functions
-4 -3 -2 -1 0 1 2 3 4
-10
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-6
-4
-2
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y=2^xy=-2^x
Horizontal translations of exponential functions
Vertical translations of exponentialfunctions
Dilation from the x-axis
Dilation from the y-axis
Examples
Examples
Calculator time.