Algebra I Chapter 8 Review

1) A population of bacteria triples in size every 5 hours. Chapter 8 Review 1) A population of bacteria triples in size every 5 hours. If the initial population of the bacteria is 125 cells, what will the population be after 15 hours? If the initial population of the bacteria is 125 cells, what will the population be after 25 hours? Model the bacteria population with an exponential function.

Answer 1) A population of bacteria triples in size every 5 hours. Chapter 8 Review 1) A population of bacteria triples in size every 5 hours. If the initial population of the bacteria is 125 cells, what will the population be after 15 hours? If the initial population of the bacteria is 125 cells, what will the population be after 25 hours? Model the bacteria population with an exponential function. 3,375 cells 30,375 cells y = 125 · 3x where x is the number of 5 hour cycles

2) Write each in scientific notation. 34,000,000 0.00063 123.456 Chapter 8 Review 2) Write each in scientific notation. 34,000,000 0.00063 123.456

2) Write each in scientific notation. 34,000,000 0.00063 123.456 Answer Chapter 8 Review 2) Write each in scientific notation. 34,000,000 0.00063 123.456 = 3.4  107 = 6.3  10-4 = 1.23456  102

3) Write each in standard notation. 8.05  106 4.25  10-4 Chapter 8 Review 3) Write each in standard notation. 8.05  106 4.25  10-4

3) Write each in standard notation. 8.05  106 4.25  10-4 Answer Chapter 8 Review 3) Write each in standard notation. 8.05  106 4.25  10-4 = 8,050,000 = 0.000425

3) Simplify using positive exponents. (x-2y-4)-3(y7y3) (2x5)3 4x-1y8 Chapter 8 Review 3) Simplify using positive exponents. (x-2y-4)-3(y7y3) (2x5)3 4x-1y8 a6 -3 a7

Answer 3) Simplify using positive exponents. (x-2y-4)-3(y7y3) (2x5)3 Chapter 8 Review 3) Simplify using positive exponents. (x-2y-4)-3(y7y3) (2x5)3 4x-1y8 a6 -3 a7 = x6y12y10 = x6y22 8x15x 2x16 = = 4y8 y8 a-18 a21 a3 = = = a-21 a18

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

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

5) Graph. Label each growth or decay. y = 2 · 3x f(x) = 4 · (0.2)x Chapter 8 Review 5) Graph. Label each growth or decay. y = 2 · 3x f(x) = 4 · (0.2)x

5) Graph. Label each growth or decay. y = 2 · 3x f(x) = 4 · (0.2)x Answer Chapter 8 Review 5) Graph. Label each growth or decay. y = 2 · 3x f(x) = 4 · (0.2)x growth decay

Chapter 8 Review a) What is the half life of this substance? b) Estimate an exponential equation that models the graph.

Answer Chapter 8 Review a) What is the half life of this substance? b) Estimate an exponential equation that models the graph. ≈ 20 minutes y = 100·0.966x y = 100·bx  50 = 100·b20  0.5 = b20  b = 20th root of 0.5  b ≈ 0.966