Growth and Decay: Integral Exponents

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Growth and Decay: Integral Exponents Section 5-1 Growth and Decay: Integral Exponents

Exponential Growth and Decay Look at examples and graphs on page 169-170

Exponential Growth and Decay Formula Where is the initial amount, the amount at time t = 0, and r is the growth rate (the percent changed to a decimal) and t is the time. If r > 0, then the initial amount grows exponentially. If -1 < r < 0, then the initial amount decays exponentially.

Laws of Exponents Same Bases: 1. 2. 3. If b ≠ 0, 1, or -1, then if and only if x = y.

Laws of Exponents Same Exponents: 4. 5. 6. If x ≠ 0, a > 0, and b > 0, then if and only if a = b.

Laws of Exponents Power of a Power: 7.

Definition of If Law 1 is to hold for y = 0, then we have . Since behaves like the number 1, we define it to be 1: =1 (b ≠ 0)

Definition of If Law 1 is to hold for y = -x and b ≠ 0, then we have . Since and have a product of 1, they are reciprocals of each other. Therefore we define: (x > 0 and b ≠ 0)

Additional Example: In a certain city, the value of a house is increasing at a rate of 16% annually. Find the value of a $100,000 house in 4 years In how many years will the value of the house be approximately double what it is now?

Example Simplify each expression.

Example Simplify each expression.

Additional Example: Simplify by using powers of the same base. a. b.