1. Algebra I Unit 7 Review

2. Unit 7 Review 1)A population of bacteria triples in size every day. a) Model the bacteria population with an exponential function. b)If the initial population of the bacteria is 125 cells, what will the population be after 25 days?

3. 1)A population of bacteria triples in size every 5 days. a) Model the bacteria population with an exponential function. b)If the initial population of the bacteria is 125 cells, what will the population be after 25 days? Unit 7 Review Answer 30,375 cells y = 125 · 3 x where x is the number days

4. Unit 7 Review

5. Answer = 25 1/2 = 27 1/3 = x 3/4

6. Unit 7 Review 3)Simplify using positive exponents. a) (x -2 y -4 ) -3 (y 7 y 3 ) b) (2x 5 ) 3 4 x -1 y 8 c) a 6 -3 a 7

7. Unit 7 Review 3)Simplify using positive exponents. a) (x -2 y -4 ) -3 (y 7 y 3 ) b) (2x 5 ) 3 4x -1 y 8 c) a 6 -3 a 7 Answer = x 6 y 12 y 10 = x 6 y 22 8x 15 x 2x 16 = 4y 8 y 8 a -18 a 21 a 3 = = = a -21 a 18

8. Unit 7 Review 4)Write an exponential function to model each situation (for x years). Find each amount after the specified time. a) $200 principal 5 years 4% compounded annually b) $3000 investment 3 years 8% loss each year

9. Unit 7 Review 4)Write an exponential function to model each situation (for x years). Find each amount after the specified time. a) $200 principal 5 years 4% compounded annually b) $3000 investment 3 years 8% loss each year Answer y = 200·1.04 x = $243.33 y = 3000·0.92 x = $2336.06

10. Unit 7 Review 5)These graphs show functions in the form y = a(b) x. a.Which graph has b < 1? b.Which axis is an asymptote in Graph B? c.What is the value of a in Graph A?

11. 5)These graphs show functions in the form y = a(b) x. a.Which graph has b < 1? b.Which axis is an asymptote in Graph B? c.What is the value of a in Graph A? Unit 7 Review Answer Graph B x-axis a = 2

12. Unit 7 Review 6)a) What is the half life of this substance? b) Estimate an exponential equation that models the graph.

13. Unit 7 Review 6)a) What is the half life of this substance? b) Estimate an exponential equation that models the graph. Answer ≈ 20 minutes y = 100·0.966 x y = 100·b x  50 = 100·b 20  0.5 = b 20  b = 20 th root of 0.5  b ≈ 0.966