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Warmup Write the following numbers as decimals and percents 1. 2. 3. 1 Standard 6.3 Writing Exponential Equations Standard 6.3 Developing: Given and equation, identify the growth/decay factor, the growth/decay rate and the initial value. Proficient: Write exponential growth and decay models from context and make predictions. 2 Identify if the equation shows growth or decay then identify the growth/decay factor and the initial value. 1a. 1b. 1c. growth/decay: factor: initial value: 3 Percent means "per hundred", or, the fraction over 100 Examples: 2a. 1 = 2b. 2 = 2c. 0.6 = To compare numbers using percents, divide the second number by the first number, then multiply by 100% Examples: 2d. 1st Value: 1 2nd value: 2 2e. 1st Value: 3.0 2nd value: 3.6 2f. 1st Value: 2.4 2nd value: 1.8 4 5 Percent Increase is the amount more than 100% of one number compared to another. How to calculate: Divide the 2nd number by the 1st, then multiply by 100%, then subtract 100%. Examples: st 2g. 1 Value: 1 2nd value: 2 2h. 1st Value: 3.0 2nd value: 3.6 2i. 1st Value: 0.8 2nd value: 4.0 6 Percent Decrease is the amount less than 100% of one number compared to another. How to calculate: Divide the 2nd number by the 1st, then multiply by 100%, then subtract from 100%. Examples: st 2g. 1 Value: 2 2nd value: 1 2h. 1st Value: 4.0 2nd value: 3.6 2i. 1st Value: 8.0 2nd value: 0.8 What if the two numbers are the same? 7 Exponential Growth Rate In exponential functions the growth factor is the ratio of outputs. For example: Growth factor: Ratio of Outputs: Percent Increase: Decimal Increase: 8 Exponential Growth Rate The exponential growth rate ( r ) is the decimal or percent increase of the output values. To calculate r in percent: Find the growth factor, multiply by 100%, then subtract 100% To calculate r as a decimal: Find the growth factor then subtract 1 To relate to growth factor ( b ): Percent: Decimal: Examples: Growth factor b, growth rate r (% and decimal) 3a. 3b. 3c. For an exponential equation to show growth, what is true about the growth factor? 9 Exponential Decay Rate In exponential functions the decay factor is the ratio of outputs. The exponential decay rate ( r ) is the decimal or percent decrease of the output values. To calculate r in percent: Find the decay factor, multiply by 100%, then subtract from 100% To calculate r as a decimal: Find the decay factor then subtract from 1 To relate to decay factor ( b ): Percent: Decimal: Examples: Decay factor b, decay rate r (% and decimal) 3a. 3b. 3c. For an exponential equation to show decay, what is true about the decay factor? 10 Summary For a : Initial value If b > 1 : Growth then b: Growth factor and r: Growth rate b = 1 + r If b < 1 : Decay then b: Decay factor and r: Decay rate b = 1 r 11 12 13 Classwork Homework H63B 14 15