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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