Properties of Exponents
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1 Name Period Unit 6 Exponents Notes lgebra Mrs. Fahey Properties of Exponents 1 Property Formula Example Product Rule m n a a Power Rule m n a ) Power of a Product Rule ab) n Quotient Rule m Power of a Quotient Rule a n a n a b Zero Exponent Rule 0 a Negative Exponent Rule n a Fractional Exponent Rule m n a ***Never leave a exponent*** Exponential Growth Exponential Decay
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7 Exponential Growth and Decay population of 100 bacteria doubles every hour. Fill in the table Time Population = 2 is known as the or. Exponential Function, where, and. Ex y = 2 x x y What happens to the graph as x gets bigger goes to the right)? What happens to the graph as x gets smaller goes to the left)? Do you think the graph will ever cross the x-axis? In order for this to happen, there must be an x-value that will make y negative. Is this possible? 7
8 General Characteristics of x-h y = ab + k Shifted h units Shifted k units To graph Determine if it is exponential growth or decay, and what transformations are occurring Find two points on the graph when x=0, and when x=1) Graph Ex f x) = 3 x+4 5 Ex x+ 1 æ1 ö f x) = ç + 1 è4 ø 8
9 If, and, then it is an exponential growth function. It is often represented by the function, where 1+r) is the growth factor, and a is the initial amount. The domain is and the range is. If, and, then it is an exponential decay function. It is often represented by the function, where 1-r) is the decay factor, and a is the initial amount. The domain is and the range is. Find the multiplier 1. 9% growth % decay 3..1% growth 4. 15% decay Ex Label as growth or decay x æ3 ö 1. y = 4 ç 2. è 4 ø x æ5 ö y = 3 ç è 2 ø x æ2 ö 3. y = -8 ç 4. è 3 ø y = -2 3) x Ex 75 bacteria double every 30 minutes. Find the population after 2 hours. Ex In 1990 the cost of tuition at a state university was During the next 8 years tuition rose 4% each year. Write a model expression. Ex Predict the population to the nearest hundred thousand, for the year 2010, if the population was 248,718,301 in 1990, and if it is projected to grow at a rate of 8% per decade. 9
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