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Algebra II Honors Review Show all work Name:______________________________ Date:____________________ Per:______ Solve the following system of equations. (7 points each) 1. 2x – 3y = 11 2. 2x + 2y = 6 4x + 2y = 10 1. (4, –1) 2. (1, 3) x + 3y = 10 3. (4, –3) 3. x + 4y = –8 4. 3x + 2y = 6 5. 10x – 9y = 15 6. 5x – 4y = 10 3x – 5y = 6 2x – 4y = 4 4. (2, 0) 3x – 2y = –31 5. (6, 5) 5x + 6y = 23 Use the zero products property to find solutions for x in the following polynomial equations. (15 points each) 7. x3 + 3x2 – 18x = 0 8. x3 + x2 = 20x 9. The number of bacteria in a colony is growing exponentially. At 2 pm there were 100 bacteria in a petri dish. At 4 pm there were 4000. Part 1:(14 points) Write an exponential function to model the population y, of bacteria x hours after 2 pm. y = abx so at the start (x = 0) we have 100 bacteria or 100 = ab0 or 100 = a y = 100bx after 2 hours (4pm or x = 2) we have 4000. So 4000 = 100b2 40 = b2 or b = 6.32 So y = 100(6.32)x Part B:(14 points) How many bacteria were there at 7 pm. y = 100(6.32)x x = 7pm – 2pm = 5 hours y = 100(6.32)5 = 100(10082.898)= 1,008,289.8 6. (–5, 8) 7. { –6, 0, 3} 8. { –5, 0, 4} 9. Pt1: y = 100(6.332)x Pt B: ~1,008,290