C 3 Chapter 3 Exponential and Log Functions

C 3 Chapter 3: Exponential and Log Functions Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Last modified: 26 th October 2015

x -2 -1 8 0 y 0. 25 ? 0. 5 ? 1 2 1 ? 2 ? 4? 3 8? 6 This is known as an exponential function. It is useful for modelling things like: population growth/savings with compound interest. ? 4 2 -2 -1 1 -2 -4 -6 2 The key property of exponential growth is that: 3 the output 4 gets multiplied 5 6 by some 7 constant each time the input increases (by a unit). e. g. A rabbit population might get 40% larger each year. ? This is in contrast to linear growth where we add some constant each time. Click to Brosketch

Gradients of Exponential Functions Function Gradient > > > Can you estimate the base of the exponential function where the gradient function is the same as the function itself?

“The” Exponential Function Gradient > > >

Bernoulli’s Compound Interest Problem (This won’t be examined) You have £ 1. If you put it in a bank account with 100% interest, how much do you have a year later? What if the interest is split into 2 instalments of 50% interest, how much will I have? What about 3 instalments of 33. 3%? And so on… No. Instalments Money at Maturity ? ? ?

Examples 1 Sketch graphs of: ? ? ? d) Sketch the function. 2 ? ? ? ?

Test Your Understanding ? ? ? ?

Inverse of Exponentials In C 2, we learnt what the inverse is of an exponential function. 4 1024 4 81 4 54. 59 5√x ? 4 log? 3 x 4 log? e x 4

Solving Equations Solve the following: E 1 E 4 ? ? E 2 E 5 ? ? E 6 E 3 ? ?

Test Your Understanding Edexcel C 3 June 2012 Q 6 ? ? ? ? e) ?

More Practice 4 1 June 2007 Q 1 ? ? 2 Jan 2007 Q 6 ? ? 3 June 2006 Q 4 ? ?

Exercises 5 Exercise 3 B ? 1 ? ? f i ? 6 3 ? ? 4 a b c ? ? ? ? ? ?