Download GROWING, GROWING, GROWING Notes – Investigations 1 and 2

GROWING, GROWING, GROWING Notes – Investigations 1 and 2 and 3
Exponential Relationships
In exponential relationships, repeated multiplication is the pattern, unlike linear relationships
where repeated addition is the pattern.
Exponential relationships graph as a curve, unlike linear relationships that graph as a line
Numbers can be written in standard form, exponential form, or factored form.
Example: 16 is standard form; 2x2x2x2 is factored form ;
24 exponential form
In the expression 3 5, the 3 is called the BASE and the 5 is called the EXPONENT or POWER
Scientific Notation - when a number is written in the form of a single digit to the left of the
decimal point times a power of 10.
Examples: 234 = 2.34 x 10 2
4,000 = 4 x 10 3
2,456,000 = 2.456 x 10 6
Scientific Notation to Standard Notation
2.6 x 10 6 = 2,600,000
4 x 10 2 = 400
1.3 x 10 5 = 130,000
GROWTH FACTOR – the number that is multiplied repeatedly in an exponential relationship
In the equation y = 200 ( 3 x )
y – the dependent variable
200 – the start number
3 – growth factor
x – exponent ( tells how many times the growth factor
is multiplied)
Examples of Exponential Growth Tables
x
1
2
3
4
5
y = 2 x–1
y
1
2
4
8
16
y= ½(2n)
x
0
1
2
3
4
5
y
1/2
1
2
4
16
32
y = 25 ( 3 x )
x
0
1
2
3
4
Start number ½ Growth factor 2
y
25
75
225
675
2,025
Start number 25
Growth Factor 3
Investigation 3
Growth rate – percent increase
Examples:
Growth Factor
1.6
1.7
1.03
1.1
Growth Rate
60 %
70 %
3%
10 %
To find the growth rate when the growth factor is known, you change the growth factor to a
percent and subtract 100 %
To find the growth factor when the growth rate is known, you add 100 % and change the
percent to a decimal.
Compound Growth – When a value is increased based on the previous value instead of the
Initial value.
Example:
$ 1,000 principal
Simple Interest
$ 1,000
$ 100
100
100
100
10 % increase.
Compound Interest
$ 1,100
1,200
1,300
1,400
$ 1,000
$ 100.00
110
121
133
$ 1,100
1,210
1,331
1,464