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