1 Exponents CHAPTER. 1. Simplify each expression. Write your answer in exponential notation.

Transcription

1 CHAPTER 1 Exponents 1. Simplify each expression. Write your answer in exponential notation. a) ( 5 ) b) ( 7 7 ) c) 4 4 ( 0.2) ( 0.5) 5 5 ( 0.5) ( 0.2) d) Simplify each expression. Write your answer using a positive exponent. a) 4 ab b) 4b 2 (3a 2 b 5 ) c) ( ) g k g k 3 d) 64a b 64ab Enrichment Course 3 1

2 Solve. Show your work. 3. A cuboid is made up of x number of small cubes with sides 1.2 inches. Given that the volume of the cuboid is 58.8 cubic inches, find x. 4. When an amoeba colony divides, its new population can be determined by multiplying the population before the division by two. a) If the initial population of an amoeba colony is 160, what is the population of the colony after it has divided 4 times? b) How many divisions need to occur for the population of amoeba to increase from 160 to 40,960? 2 Chapter 1 Exponents

3 5. The thickness of a paper is doubled each time it is folded. The initial thickness of a piece of paper is 0.38 millimeter. a) What is the total thickness of the paper after it has been folded 7 times? b) If the final thickness of the paper is millimeters, how many times has the paper been folded? 6. The following numbers form a sequence to a code: 3, 3 2, 3 3, 3 4,, 3 n. a) Find the 10th number in the code. b) If the last numbers in the sequence is 6,561, what is the value of n? Enrichment Course 3 3

4 7. A cylindrical-shaped cup has a height of 7 centimeters and a volume of 112p cubic centimeters. Henry fills the cup completely full of water. He then pours the water from the cup into a cone. If the cone has a radius twice the measure of the cup, what is the height of the cone? 7 cm 8. Martha bought two identical blocks of clay. Each block of clay has a volume of 64 cubic inches. Martha forms one block of clay into a sphere and she forms the other block of clay into a cube. a) Find the side length of the cube. b) Find the radius of the sphere, to the nearest hundredth. c) Which solid has a greater surface area, the sphere or the cube? Explain how you determined your answer. 4 Chapter 1 Exponents

5 9. Find the prime factorization of each number. Write your answers in exponential notation. a) 1,008 b) 864 c) Using your answers in a) and b), find the greatest common factor of 1,008 and 864. Write your answer in exponential notation. 10. The smallest human cell has a diameter of approximately meter or 10 micrometers. Assuming that each cell is a perfect sphere, find the volume of 10 trillion (10 13 ) cells. Enrichment Course 3 5

6 11. Geysers are springs of water that are ejected through the Earth s surface at various intervals depending on the temperatures beneath the Earth s volcanic rock. The table shows the approximate frequency of geyser eruptions in Yellowstone National Park. Name of Geyser Old Faithful Bead Geyser Riverside Geyser Daisy Geyser Approximate Frequency of Eruption 80 minutes 32 minutes 375 minutes 175 minutes a) Find the prime factorization of each value in the approximate frequency of eruption column. Write your answers in exponential notation b) If the four geysers erupt at the same time at 9:00 a.m., when will the next concurrent eruption take place? Hint: Find the least common multiple of the approximate eruption frequency values in the table. 6 Chapter 1 Exponents

7 12. On January 1, 2012, Julia deposits $2,500 in her savings account. It will earn 5% interest compounded yearly. a) If Julia makes no additional deposits and no withdrawals, how much money will be in her account on December 31, 2017? b) If beginning January 1, 2013, and each year thereafter, Julia deposits $200 into her bank account, how much money will be in her account on December 31, 2017? c) Given that Julia deposits $2,500 into an account, which type of account will result in a greater balance after 5 years, a 5% yearly compound interest account or a 5% yearly fixed interest account? Explain how you determined your answer. Enrichment Course 3 7