maths 083

Revise the index laws and complete the following questions for revision on indices.REVISION ON INDICES

Exponential equations or power equations represent exponential growth or decay, where change in y can be measured in small amounts at first and then in rapidly increasing amounts.  

Example:

a Construct a table of values for the exponential equation y = 3^x for x ∈ [0,10]. 

b 

Sketch a graph of y = 3^x for x ∈ [0,4]. 

Solution:

a

Example:

a Make a table of values for y = 4^−x for x ∈ [−3,1] in increments of 0.5 for values of x. 

b Sketch a graph of y = 4^−x for x ∈ [−2,1] . Why does it represent exponential decay? 

Solution:

a

b The graph shows exponential decay because, as values of x get larger, values of y rapidly get smaller at first, then the change in y is very slight. 

Example:

A new strain of bacteria is discovered in a hospital. The bacteria rapidly multiply, and a graph of the bacterium’s growth is drawn. It appears to show exponential growth. 

a How many bacteria will there be after 30 seconds? 

b How long will it take to reach 2000 bacteria? 

Solution: 

a approximately 40 bacteria                      b 1 min 30 s

 EXPONENTIAL GRAPHS 

A number is written in standard form or scientific notation when it is shown as a number between 1 and 10 multiplied by a power of 10.

When we move the decimal point to the left the power of 10 is positive.
When we move the decimal point to the right the power of 10 is negative.

Open the following link for questionsStandard form

To rationalise the denominator we multiply with a fraction with the same numerator and denominator as the denominator.

Open the link for questionsRationalising the denominator

Irrational numbers  have infinite non-repeating decimals.

For example 3.4567823…    

√11 = 3.31662..

Irrational numbers are surds

The following rules apply:

Operating with surds

OPERATING WITH SURDS

Open the following link for questionsNEGATIVE POWERS

We use the index laws to simplify numbers in index form.

Open the link for questionsINDEX LAWS

The Numbers that repeatedly multiplied can be represented in a power form or exponential form or index form.

5 is the base and 4 is the power, or exponent or index.

Example: Write the following in exponent form.
a 8 × 8 × 8 × 8 × 8

b −4 × −4 × −4

Open the following link for questionsNUMBERS IN INDEX FORM

Before we start exploring the wonderful world of indices you are required to complete the following test to determine your strengths and weaknesses. In addition you are required to construct a ‘mind map’ using your current knowledge on the topic and possibly information you can get from the internet. Good luck.

Pre- test on indices

Open the following link for the project on Statistics.

Present the project as a pod-cast. Graphs to be completed using  suitable programs.Statistics project