Unit Summary 5

Class : Algebra 1

Unit 5: Exponents and exponential functions – chapter 8

  1. Big Ideas:
  • Students will understand how to simplify and evaluate monomial expressions and formulas.
  • Students will understand that relationships can be described for mathematical situations that have numbers repeat in predictable ways.
  • Students will be able to use graphs and tables to distinguish between linear and nonlinear functions.
  • Students will understand that real world applications involving growth can be modeled using a linear growth model or an exponential growth model.
  1. Topics that will be covered:
  1. Multiplication properties of exponents
  2. Division properties of exponents
  3. Negative and zero exponents
  4. Scientific notation
  5. Exponential growth
  6. Exponential decay
  7. Graphing exponential functions
  1. Essential Questions:
  • What is simplest form?
  • How is the power rule related to the product rule?
  • What does a negative exponent mean?
  • What does it really mean to “cancel” when simplifying fractions?
  • Where can I use scientific notation and radicals in the real-world?
  • How are exponential functions different from linear functions?
  • What happens with the exponents when the same bases are multiplied or divided?
  1. Sample questions to answer by the end of the unit:

Write all answers in simplest form.

1. 2x2(3x2 – 5x – 12)2. 12x(3x – 5) – 6x(2x – 4)

3. 12x2 – 24x – 84. (2x3y7)4

4x

5. (10xy)3(4x3y)26. 12x2y9

18x7y4

Determine whether each number is written in scientific notation. If it is not, write it in scientific notation.

7. 950 x 1058. 72.35 x 109

9. 1.6 x 10710. 0.26 x 10-13

Write each expression so that all exponents are positive.

11. b-4g3d-512. x-4y8g-2

x-3y16g7

13. -83(8-5)14. (3x2y-5)-2

Solve for g.

15. g2 = 3616. 2g = 1

17. 2g = ½ 18. 2g = 0.25

Identify each function as exponential growth or exponential decay then find the percent of increase or decrease for each function.

19. y = 105  0.53x20. y = 856  1.07x

21. y = 3112  2.49x22. y = 4  0.19x

23. y = 10,000  0.48x24. y = 21  0.34x

Write an exponential function to model each situation.

25. 5,000,000,000 initial population

3.5% annual decrease

8 years

26. $2400 purchase

10% loss in value each year

9 years

27. $500 initial market value

13.2% annual increase

17 years

Calculate solutions for the following word problems.

28. A colony of 1,000 ants can increase by 15% in a month. How many ants will be in the colony after 10 months?

29. A baby weighing 7 pounds at birth may increase in weight by 11% per month. How much will the baby weigh after 1 year?

30. A deposit of $1500 in an account pays interest 7.25% compoundedannually. What is the account balance after 8 years?

31. Bacteria in a culture are growing exponentially with time as shown in the table. Write a function to show the growth of bacteria.

Day Bacteria

0 100

1 300

2900

32. The value of a stock when purchased is $10 a share.The stock decreased at a rate of 3% daily.How much is it worth after 12 days?