Patterns with Exponents: Connecting Your Knowledge

Transcription

1 Unit 3: Growing, Growing, Growing//Investigation //Connections Name Class Date Patterns with Exponents: Connecting Your Knowledge I can understand the rules for working with exponents. Math / 30 Reflection / 10 Total / 40 Points For this packet, your goal is to earn will be from the math problems. 10 will be from the reflection section. Look at the point values of the following questions and answer the questions that you feel most comfortable to answer. Find the product or quotient of powers for each of the following, using exponent notation. If the expression cannot be simplified, say so. 1. b b (z ). r r 3

2 Simplify each of the following expressions using operations with exponents. (There should not be any parentheses in your answers!) /3 8. m 3 ( m n) 4 n 7 Use the rules of exponents and scientific notation to solve the following without using a calculator. Express your answer in scientific notation! 9. (3.0 x 10 8 ) x (9.0 x 10 1 ) 10. (8.0 x 10 1 ) (.0 x 10 6 ) 11. In Civic Ville, 13,000,000 people get their produce from local farms. Those people eat a total of 3.09 x 10 8 pounds of produce each month. a. On average, how many pounds of produce does each person eat per month? b. Using your answer from part (a), how many pounds of produce does each person eat per day? (assume there are 30 days in the average month) 1. MULTIPLE CHOICE: Which of the following expressions is equivalent to 1. 10? a. (1.) (1.) b. (1.) (1.) c. (1.) 10 HOW do you know your answer is correct? (Show mathematical proof!)

3 13. Some students are trying to solve problems with rational exponents. a. Which of these students is correct? b. Why is that student correct? (Use mathematical reasoning) c. Why is the other student Incorrect? (Use mathematical reasoning) 14. The number 7 is written in standard form as 18 and in scientific notation as 1.8 x 10. The number (0.) 7 is written in standard form as and in scientific notation as 7.81 x Write each number in the table in both standard form and scientific notation. Exponential Form Standard Form Scientific Notation 8 (0.4) 8 1 8

4 1. Grandville has a population of 1,000. Its population is expected to decrease by 4% a year for the next several years. Tinytown has a population of 100. Its population is expected to increase by 4% a year for the next several years. a. What is the equation for each town s population? Grandville: Tinytown: b. What is the population of each town after. years? Grandville: Tinytown: c. Will the population of the two towns ever be the same (will their populations ever intersect )? Explain why or why not In 1803, the United States bought the 88,000-square-mile Louisiana Purchase for $1,000,000. Suppose one of your ancestors was given 1 acre of the Louisiana Purchase. Assuming an increase in value of 4% per year, what was the value of this acre in 003? (HINT: Convert miles to acres first! 640 acres = 1 square mile.)

5 Chen decides to make his ballots starting with a sheet of paper with an area of 1 square foot. a. Copy and extend this table to show the area of each ballot after each of the first 8 cuts. b. Write an equation for the area A of a ballot after any cut n. c. Use your equation to find the area of a ballot after 0 cuts. d. Write your answer from part (c) in scientific notation Use the data from Problem.4 (In your investigations packet) to answer the following questions. Write each of your final answers in scientific notation. a. How many total gallons of water are used in the United States in a year? b. About how many times greater is the amount of water used for irrigation than the amount used for livestock? c. Suppose 80% of water is from surface sources. How many gallons of freshwater are removed from the ground each month?

6 Patterns with Exponents Reflection In this investigation, you explored properties of exponents. You also looked at how the values of a and b affect the graph of y = a(b x ). You made use of scientific notation to find relations among very large numbers. Answer the following questions in complete sentences. (This reflection is worth 10 of your total of 40.) 1. Choose of the rules for operation with exponents. Explain how each of them works using complete sentences.. What are practical applications of scientific notation? (In other words, what are some realistic situations when scientific notation can be used?) 3. How does b (or the growth factor of an exponential equation) affect the graph of y = a(b x )? 4. Explain how knowing the rules of exponents assists you when solving numbers with scientific notation.. Explain how exponential functions are different from linear functions.