Ch8-2 Solving Exponential Functions
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This document discusses solving exponential equations by equating exponents. It provides examples of solving equations by making the bases the same using properties of exponents, including using negative exponents to write fractional bases as powers of an integer base. The document demonstrates these steps and techniques on sample problems, then prompts the reader to solve additional exponential equations on their own and check their work.
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Ch8-2 Solving Exponential Functions
- 2. Real World Use of Exponential Functions • • • • • Population Growth Money (Compound Interest) Depreciation (Cars) Half-Life (Radioactive Material) Bacteria Growth
- 3. Exponential Equations • One way to solve exponential equations is to use the property that if 2 powers w/ the same base are equal, then their exponents are equal. • For b>0 & b≠1 if x b = y, b then x=y
- 4. Solve by equating exponents 3x 3 9 2 2 3x 3 9 x 4 Since they have the same bases we can set their exponents equal to each other and solve for x. 34 3 Check → 2 29 29 9 2
- 5. Your turn
- 6. Solve by equating exponents 3x 4 2 8 2 3x 6x 2 x 1 3 x 1 2 3x 3 2 Distribute! Since they do NOT have the same bases…we have to rewrite so they have common bases. Common base = 2 6x 3x 3 31 x 1 4 81 1 Check → 64 64
- 7. Your turn
- 8. Solve by equating exponents 4 x 1 2 2 x 2 2 2x 2x 2 2 x 3 Common base = 2 1x 3 Distribute! x 3 How can we make ½ a base of 2? Negative exponents!!! x 3 1 2 1 Check → 4 4 x 1 1 2 4 4 22 4 1 3 2
- 9. You Try
- 10. Your turn! 9 x 3 x 2 Be sure to check your answer!!! x 2
- 11. Your turn! 3 1 x ( ) 9 x 3 Be sure to check your answer!!! x 2
- 12. Your turn! 9 x 4 27 4x Be sure to check your answer!!! x 4 5