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2. Exponential Functions Aims: To know the general formula for an exponential graph.

3. What You Need To Be Able To Do To know the general formula for an exponential graph: We have seen the functions for linear, quadratic and some general polynomial functions. After this we will take a first look at logarithms.

4. Maths Ex 7A is very weird but maybe worth a look especially Q5

5. Geometric Sequence Graph The function of a basic exponential function f(x)=b x There are some limitations however…

6. Limits of b Values b must be positive (since –b would not be defined for fractional values of x with even denominators) b cannot be 1 since that would result in every value being 1 and therefore a line. So given this information lets see some exponential graphs… On a graphical calculator with a standard viewing window plot… y=2 x y=4 x y= (½) x

7. Look

9. Summary You are expected to be familiar with the shapes of exponential graphs. You are expected to know the effect of having different values of b for the graph y=b x. To know where these graphs cross the y axis and that this is the value of k in y=kb x. Lets have a quick go…

10. Sketch Showing Points of Intersection with the Axes.

15. Sketch Showing Axes Intercepts and Asymptote

16. Sketch Showing Points of Intersection with the Axes.

17. Sketch Showing Axes Intercepts

18. Sketch Showing Points of Intersection with the Axes.

19. Logarithms Aims: To know what logarithms are. To be able to evaluate logarithms including solving equations involving logarithms.

20. What You Need To Be Able To Do Name: What is a logarithm Describe: The relationship between a n = x and Log a x Explain: How to solve basic missing value type equations that include logs.

21. Maths Ex 7B p 356

22. Inversing What is the inverse of +? What is the inverse of x? What is the inverse of √? But what is the inverse of taking 2 to the power of a number e.g. How can you make x the subject of y=2 x ? The answer is that we do not currently have an inverse for an exponential…

23. Napier John Napier of Merchiston (1550 – 4 April 1617) – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish mathematician, physicist, astronomer & astrologer, and also the 8th Laird of Merchistoun.Scottish mathematicianphysicist astronomerastrologerLairdMerchistoun John Napier is most renowned as the inventor of the logarithm, and of an invention called "Napier's bones".logarithmNapier's bones Napier also made common the use of the decimal point in arithmetic and mathematics.decimal point

24. The Logarithm The logarithm is an inverse of an exponential base it is a function that must have a base corresponding to the base it is inversing. E.g. To inverse 2 x one would have to use log base 2, written log 2. We say that we apply log n to a value (a) and the answer is the power of n that gives you a. E.g. log 2 16 = 4

25. The Logarithm Equivalence So IF 5 3 =125 then Log 5 125=3 Can you write this statement in general?

26. Solving Problems You will be expected to be able to write logarithm statements as indices and vice versa. E.g. If log 6 1296 = 4  6 4 =1296

27. Evaluating You need to be able to find the missing values in equations involving logarithms. Log 4 x = 3 what is x? Log 2 1 / 16 = y what is y? Log x 18 = 4 what is x? Log √x x 3 =a what is a?