7.1A Homework: Exponential Form* Name:

Period:

Directions: Rewrite each number in exponential form with the number two as its base. 1. 32

2. 512

Directions: Evaluate the expression for 3.

. Show all of your work. 4.

14

96

5.

6. 24

0

Directions: The following statements are incorrect. Explain in words the mistake made and write the correct answer. 7. In the expression the exponent.

, 4 is the base and 5 is

This statement is incorrect because 5 is the base and 4 is the exponent. 𝑥𝑎 Exponent Base number

8. 6 is an exponent and tells how many times the base is multiplied by itself. An exponent should not be multiplied by the base. · · ·

· ·

10 SDUHSD Math B College Prep Module #7 – TEACHER EDITION (2015-2016)

10.

9.

if 𝑥 𝑥 𝑥 𝑥 𝑥 𝑥 𝑥 𝑥 3x represents repeated addition and 𝑥 represents x multiplied by itself three times.

The base and exponent are not interchangeable.

11.

Teacher note: If you think of this geometrically, the first expression represents a rectangle with a length of 3 and a width of x; whereas the second expression represents the volume of a cube with side length x.

12. represents multiplying (-2) by itself three times.

Because there are no parentheses around -7, 7 is the base. Therefore, seven is squared first and then the outcome is multiplied by -1.

Teacher note: Discuss how an exponent affects a negative number. Remind students how they can determine the sign of the final outcome by noting whether the exponent is even or odd.

13. A candy maker is making taffy. He starts with one long piece of taffy and cuts it into 3 pieces. He then takes each resulting piece and cuts it into three pieces. He then takes each of these resulting pieces and cuts it into three pieces. He continues this process. a. How many pieces of taffy does the candy maker have after the first 4 rounds of cuts? The candy maker has 81 pieces of taffy after the first 4 rounds of cuts.

b. How many pieces of taffy will the candy maker have after 8 rounds of cuts? . The candy maker will have 6,561 pieces of taffy after 8 rounds of cuts.

c. The candy maker gets a special order for 243 pieces of peppermint flavored taffy. How many rounds of cuts will he have to make to get this many pieces?

The candy maker will have to make 5 rounds of cuts to get 243 pieces of taffy.

11 SDUHSD Math B College Prep Module #7 – TEACHER EDITION (2015-2016)

14. Your school is selling raffle tickets. You bought one ticket and found out that you are the winner! The cool thing about this raffle is you have a choice of two prize options: Option #1: $5,000 cash Option #2: For the month of April you would get 1 cent on April 1st, 2 cents on April 2nd, 4 cents on April 3rd, 8 cents on April 4th, and so on for all 30 days in April. a. Make a prediction of which option you should pick and explain in words why you predict that option. Students may choose Option #1 here since $5,000 may seem bigger to them than a bunch of pennies. Those who understand the power of exponents may choose 0ption #2 from the start. b. Fill out the table below to represent Option #2: Date April 1 April 2 April 3 April 4 April 5 April 6 April 7 April 8 April 9 April 10 April 11 April 12 April 13 April 14 April 15 April 16 April 17 April 18 April 19 April 20 April 21 April 22 April 23 April 24 April 25 April 26 April 27 April 28 April 29 April 30

Amount of Money Today Earned (cents) 1 2 4 8 16 32 64 128 256 512 1,024 2,048 4,096 8,192 16,384 32,768 65,536 131,072 262,144 524,288 1,048,576 2,097,152 4,194,304 8,388,608 16,777,216 33,554,432 67,108,864 134,217,728 268,435,456 536,870,912

c. On the very last day of April, if you choose Option #2, how many pennies would you get paid? How much is this in dollars? 536,870,912 pennies 5,368,709.12 dollars

d. Compute the TOTAL amount of money that you would make over the thirty days of April if you choose Option #2. Amount in pennies: 1,073,741,823 pennies

Amount in dollars: 10,737,418.23 dollars

e. Which option is the better option for you to choose? Option #2 would be more money

f. Write an algebraic expression that represents the number of pennies you would receive on any given day. 𝑛

, where n is the number of days

12 SDUHSD Math B College Prep Module #7 – TEACHER EDITION (2015-2016)

Spiral Review: 15. Solve the equation:

(

)

16. Write the equation of a graph that is shifted 9 units to the right from the graph of |

| | and opens down.

|

17. An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. Admission plus five rides cost $16. What is the charge for admission and the cost of a ride? Write a system of linear equations to solve and show all of your work. The cost of one ride is $2 and admission is $6.

18. The perimeter of a square is a function of its side length. What type of function does it represent? Explain your reasoning. It represents a linear function because the equation f(x) = 4x has a constant rate of change.

19. Write the equation of a line in slope-intercept form that is perpendicular to the y-axis and passes through the point (-4,9) y=9

20. Fill in the blank with always, sometimes or never. a. Dilations produce a pre-image and image that are always b. Linear relations

c. Quadratic functions

sometimes

never

the same shape but a different size.

represent functions.

have a degree of three.

13 SDUHSD Math B College Prep Module #7 – TEACHER EDITION (2015-2016)