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# 5 1 integral exponents

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### 5 1 integral exponents

1. 1. Objectives: 1. Review exponential growth and decay 2. Simplify expressions containing integral exponents
2. 2. Functions describing quantities that increase/decrease by a given rate (percentage) over time. Modeled by: where A0 is initial amount (at t = 0) and r is the growth rate. If r > 0, exponential growth If -1 < r < 0, exponential decay
3. 3. Suppose that a radioactive isotope decays at a rate of 15% per day. If 40 kg are present now, find the amount present: 6 days from now 6 days ago
4. 4. The cost of a hamburger has been increasing at a rate of 9% per year. If the cost is now \$4, find the cost of a hamburger: 5 years from now 5 years ago
5. 5. Same Bases   If a ≠ 0, 1, or -1, then and only if m = n. if
6. 6. Same Exponents    If m ≠ 0, a > 0, and b > 0, then if and only if a = b.
7. 7. Power of a Power  And…  
8. 8. A simplified expression contains no negative exponents or powers of powers.
9. 9. Simplify:
10. 10. Simplify:
11. 11. Simplify:
12. 12. Simplify:
13. 13. Write as a power of b:
14. 14. Write as a power of b: