Growth Factor The base number in an exponential relationship. The base number in an exponential relationship. The constant factor that each value is multiplied.

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Presentation transcript:

Growth Factor The base number in an exponential relationship. The base number in an exponential relationship. The constant factor that each value is multiplied by to get the next value. The constant factor that each value is multiplied by to get the next value. Example:Example: A = 25(3 x ) A = 25(3 x ) The growth factor is 3 The growth factor is 3

How to find the Growth Factor from a table Divide a y-value by the previous y-value. Divide a y-value by the previous y-value. Example:Example: Xy divided by 100 = divided by 300 = 3 The growth factor is 3

Growth Rate The percent increase in an exponential relationship. The percent increase in an exponential relationship. Example: The number of rabbits increased from 100 to 180, an 80% increase.Example: The number of rabbits increased from 100 to 180, an 80% increase. The growth rate is 80% The growth rate is 80% Written as a decimal, this is.80 Written as a decimal, this is.80 Interest is a growth rate Interest is a growth rate

How do I find growth rate if I know the growth factor? Subtract 1 from the growth factor to get the growth rate. Subtract 1 from the growth factor to get the growth rate. Example: If the growth factor is 1.2, the growth rate is 1.2 – 1 =.2 or 20%.Example: If the growth factor is 1.2, the growth rate is 1.2 – 1 =.2 or 20%.

How do I find the growth factor if I know the growth rate? Add 1 to the growth rate. Add 1 to the growth rate. Example: If the growth rate is 70% (.70) add a 1 to the front of that.Example: If the growth rate is 70% (.70) add a 1 to the front of that. The growth factor is 1.7. The growth factor is 1.7.

What do I do with a growth factor or growth rate? If you have an initial value (y-intercept), knowing the growth factor or growth rate will help you find subsequent values. If you have an initial value (y-intercept), knowing the growth factor or growth rate will help you find subsequent values. Example: I have $500 in the bank. If I earn 5% interest for 5 years (compound growth), how much will I have at the end of 5 years?Example: I have $500 in the bank. If I earn 5% interest for 5 years (compound growth), how much will I have at the end of 5 years?

Example: Initial value at beginning of year Growth rate value (5%) Value with growth factor (1.05) $500$25$525 $525$26.25$ $551.25$27.56$ $578.81$28.94$ $607.75$30.39$638.14

Practice What is the growth factor for a yearly increase of 7%? What is the growth factor for a yearly increase of 7%? What is the growth factor for a yearly increase of 40%? What is the growth factor for a yearly increase of 40%?

Practice What is the growth rate associated with the growth factor of 1.3? What is the growth rate associated with the growth factor of 1.3? 30%30% What is the growth rate of an investment with a growth factor of 1.08? What is the growth rate of an investment with a growth factor of 1.08? 8%8%