C3 Chapter 3: Exponential and Log Functions Dr J Frost Last modified: 1 st August 2014

x y ?????? Click to Brosketch This is known as an exponential function. It is useful for modelling things like: population growth/savings with compound interest. The key property of exponential growth is that: the output gets multiplied by some 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. ? ?

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 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. InstalmentsMoney at Maturity ? ? ? ? ?

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

Test Your Understanding ? ? ? ?

Inverse of Exponentials In C2, we learnt what the inverse is of an exponential function. 4 5 √x ? 4 log 3 x 4 81 ? 4 log e x ?

Solving Equations Solve the following: E1 E2 E3 E4 E5 E6 ? ? ? ? ? ?

Test Your Understanding Edexcel C3 June 2012 Q6 e) ? ? ? ? ?

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