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# Ch8-2 Solving Exponential Functions

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### Ch8-2 Solving Exponential Functions

1. 1. Solving Exponential Equations
2. 2. Real World Use of Exponential Functions • • • • • Population Growth Money (Compound Interest) Depreciation (Cars) Half-Life (Radioactive Material) Bacteria Growth
3. 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. 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
6. 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
8. 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. 9. You Try
10. 10. Your turn! 9 x 3 x 2 Be sure to check your answer!!! x 2
11. 11. Your turn! 3 1 x ( ) 9 x 3 Be sure to check your answer!!! x 2
12. 12. Your turn! 9 x 4 27 4x Be sure to check your answer!!! x 4 5
13. 13. H/W p.488 #9,10,12,14,32,33