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EXAMPLE 4

b. Write a power function y = ax whose graph passes through (3, 2) and (6, 9). Substitute the coordinates of the two given points into y = ax. b. b. 2 = a 3. b. 9 = a 6. EXAMPLE 4. Write a power function. SOLUTION. STEP 1. Substitute 2 for y and 3 for x.

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EXAMPLE 4

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  1. b Write a power function y = axwhose graph passes through (3, 2) and (6, 9) . Substitute the coordinates of the two given points into y = ax. b b 2 = a 3 b 9 = a 6 EXAMPLE 4 Write a power function SOLUTION STEP 1 Substitute 2 for yand 3 forx. Substitute 9 for yand 6 forx.

  2. Solve for ain the first equation to obtain a= , and substitute this expression for ain the second equation. Log 4.5 2 Substitute for ain second equation. b 9 = 6 b Log2 3 2 3 b Log 4.5 = b 2 b Take log of each side. 2 9 = 2 2 b 4.5 = 2 2 3 b = b 2.17 b EXAMPLE 4 Write a power function STEP 2 Simplify. Divide each side by 2. Change-of-base formula Use a calculator.

  3. 2 3 2.17 2.17 Determine that a = 0.184. So, y = 0.184x. EXAMPLE 4 Write a power function STEP 3

  4. b Write a power function y = ax whose graph passes through the given points. for Example 4 GUIDED PRACTICE 5. (2, 1), (7, 6)

  5. b Write a power function y = ax whose graph passes through the given points. Substitute the coordinates of the two given points into y = ax. b b 4 = a 3 b 15 = a 6 for Example 4 GUIDED PRACTICE 6. (3, 4), (6, 15) SOLUTION STEP 1 Substitute 4 for yand 3 forx. Substitute 15 for yand 6 forx.

  6. Solve for ain the first equation to obtain a= , and substitute this expression for ain the second equation. b 15 = 6 15 4 Substitute for ain second equation. b 3 4 b 15 = 4 2 b = 2 4 3 b Log 3.7 = b 2 Take log of each side. 4 2 3 b for Example 4 GUIDED PRACTICE STEP 2 Simplify. Divide each side by 4. 3.7 = 2

  7. 4 3 1.9 1.91 = 1.9 Determine that a = 0.492. So, y = 0.492x. 0.5682 Log 3.7 Log2 0.3010 = b 1.90 b for Example 4 GUIDED PRACTICE Change-of-base formula Simplify. Use a calculator. STEP 3

  8. b Write a power function y = ax whose graph passes through the given points. Substitute the coordinates of the two given points into y = ax. b b 8 = a 5 b 34 = a 10 for Example 4 GUIDED PRACTICE 7. (5, 8), (10, 34) SOLUTION STEP 1 Substitute 8 for yand 5 forx. Substitute 34 for yand 10 forx.

  9. Solve for ain the first equation to obtain a= , and substitute this expression for ain the second equation. b 34 = 10 17 8 Substitute for ain second equation. b 5 4 b 34 = 8 2 b = 2 8 5 b Log 4.2 = b 2 Take log of each side. 8 2 5 b for Example 4 GUIDED PRACTICE STEP 2 Simplify. 4.2 = 2

  10. = b Log 4.2 0.6284 Log2 0.3010 2.09 Determine that a =0.278. So, y = 0.278x. = b 2.09 b for Example 4 GUIDED PRACTICE Change-of-base formula Simplify. Use a calculator. STEP 3

  11. for Example 4 GUIDED PRACTICE 8.REASONINGTry using the method of Example 4 to find a power function whose graph passes through (3, 5) and (3, 7). What can you conclude? SOLUTION The points cannot form a power function.

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