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CMIC 2/3 Unit 5 Warm Up The operating cost of a store that sells only ipods can be modeled as a function of the number of ipods that the store purchases from the supplier. The rule for that function is: C(x) = 3500 + 35x Evaluate and explain the meaning of: C(5) C(20) C(x) = 4095 S(x)=4000 – 250x Evaluate S(10) S(x)=4000 – 250x Evaluate S(10) S(10) = 4000 – 250(10) S(10) = 1500 S(x)=4000 – 250x Evaluate S(x) = 1000 S(x)=4000 – 250x Evaluate S(x) = 1000 1000 = 4000 – 250x -4000 -4000 -3000 = -250x -250 -250 12 = x Rewrite in Standard Form (x + 5)(x – 2) Rewrite in Standard Form (x + 5)(x – 2) x2 – 2x + 5x – 10 x2 + 3x – 10 Factor the following x2 + 8x – 20 Factor the following x2 + 8x – 20 -20 -2 10 8 (x + 10)(x – 2) Find the x-intercept (zeros) x2 + 8x + 15 Find the x-intercept (zeros) x2 + 8x + 15 15 5 3 8 (x + 5)(x + 3) x + 5 = 0 x = -5 x+3=0 x = -3 Find the vertex (minimum or maximum x2 + 8x + 15 Find the vertex (minimum or maximum x2 + 8x + 15 a=1 b=8 c = 15 -b/2a = -8/2 = -4 (-4)2 + 8(-4) + 15 = -1 vertex = (-4, -1) Find the y-intercept and Graph x2 + 8x + 15 Find the y-intercept and Graph x2 + 8x + 15 y- int = 15 Solve using the quadratic formula 3x2 – 10x + 7 =0 6x2 + 7x – 10 = -5 Common Logs … Calculate the following: log 1000 log 0.001 log 78 Explain why the answer makes sense Problem 1 Solve the following: log 1000 Problem 1 Solve the following: log 1000 = 3 Problem 2 Solve the following: log 0.001 Problem 2 Solve the following: log 0.001= -3 Problem 3 Solve the following: log -71 Problem 3 Solve the following: log -71= no solution Problem 4 Explain why the following statement is true: log 100 = 2 Problem 4 Explain why the following statement is true: log 100 = 2 It is true because 102 = 100. Problem 5 Explain why the following statement is true: 1 < log 65 < 2 Problem 5 Explain why the following statement is true: 1 < log 65 < 2 It is true because 65 is between 10(101) and 100 (102). This is true because the log of 65 is 1.812 which is between the numbers 1 and 2. Problem 6 Explain why the following statement is true: log 0.1 = -1 Problem 6 Explain why the following statement is true: log 0.1 = -1 It is true because 10-1 = 0.1. Problem 7 Solve the following equation: 10x = 45 Problem 7 Solve the following equation: 10x = 45 log 10x = log 45 x = 1.653 Problem 8 Solve the following equation: 104x = 0.457 Problem 8 Solve the following equation: 104x = 0.457 log 104x = log 0.457 4x = -.34 4 4 x = -.085 Problem 9 Solve the following equation: 10x+3 = 6730 Problem 9 Solve the following equation: 10x+3 = 6730 log 10x+3 = log 6730 x + 3 = 3.828 -3 -3 x = 0.828 Problem 10 Solve the following equation: 6(102x )= 600 Problem 10 Solve the following equation: 6(102x )= 600 102x = 100 log 102x = log100 2x = 2 x=1 Problem 11 Complete the table: x 0.5 1 5 10 log(x) Problem 11 Complete the table: x log(x) 0.5 -0.3 1 0 5 0.699 10 1 Warm Up Solve each equation: 10x = 63 104x = 320 10x+2 = 2700 (Hint: Use logarithms to help solve) Warm Up Solve each equation: 10x = 68 103x = 0.587 10x+2 = 7820 (Hint: Use logarithms to help solve) #8 p.385 #9 p.385