L E S S O N M A S T E R. Name. Vocabulary. 1. In the expression b n, b is called the?.

Transcription

1 Vocabulary 7- See pages 7-7 for objectives.. In the epression b n, b is called the?.. The identity function f has the equation f()?.. If g(), is g an eample of a power function? Why or why not?. In a game with a friend, Felipe has a 7 chance of winning a round, and each round is independent. Suppose Felipe and his friend play si rounds. What is the probability that Felipe will win all si rounds? Representations Objective I. Multiple choice. Which of the following could be a graph of an odd power function? (a) y (b) y (c) y. The point (-, -) is on the graph of an odd power function. a. What other point must be on the graph? b. Write an equation for this function. 7. a. On the grid at the right, sketch graphs of f() and g(). b. For what values(s) of is f() g()? y g() f() c. For what values of is f() > g()? - - 8

2 7- See pages 7-7 for objectives. Skills Objectives and B In 9, simplify.. ( ). (w ). 7y 8y c. -.. c 9 (z ) z 8 b b 9 b b (-9z ) 9 z p p 0 0 v ( ) ( ) v In 0, evaluate. 0. () 0. ( ) ().. () In 7, true or false. If false, rewrite to be true.. (q ) q 0. (m 0 y 7 ) m 0 y. r r r 7 7. z Properties Objective F 8. In 98, the U.S. population was roughly. 0 8 people, while water usage was approimately 0 gallons per day. Estimate the number of gallons of water used per person daily in the U.S. in 98. z 9 z 9. Jupiter s largest moon, Ganymede, is the largest moon of any planet in our solar system, with a diameter of about.7 0 km. Estimate Ganymede s volume. 9

3 7- See pages 7-7 for objectives. Skills Objectives and B In, write as a decimal or a simple fraction ( ) (-8) -.. (7 - ) In 7, simplify the result using only positive eponents y - 7y 9. (m - ) 0. ( - z ) (z - y) f h f h. ( ) - ( ). 7 - g 7 g -9. True or false. For any positive base b and any real eponent n, b -n -(b n ). If true, prove the statement. If false, provide a countereample.. The Law of the Lever states that the distance d of a person from the fulcrum varies inversely as his or her weight w. a. Write this variation equation with positive eponents. b. Write this variation equation with negative eponents.. In Caroline s pinhole camera, the radius of the pinhole is. 0 - mm. Find the area of the pinhole, the region through which light can reach the film. 70

4 Uses Objective G 7- See pages 7-7 for objectives.. Yu invested $00 in a savings account that pays.% interest compounded annually. How much money will be in his account after years if no deposits or withdrawals take place during the years?. Debbie invested $,000 in a -year CD (certificate of deposit) that pays 7.8% interest compounded quarterly. The CD matures net February. If no deposits or withdrawals took place during the -year period, how much will the CD be worth when it matures?. Maria invested $000 in an IR (individual retirement account) years before she planned to retire. With a % annual yield, if Maria makes no deposits or withdrawals during the years, what will be the value of the IR when it matures?. Suppose that you plan to put $000 in a credit-union savings account for two years at % interest compounded daily. Shoreline Credit Union compounds 0 days a year; South Side Credit Union compounds days a year. How much more money will you earn if you invest at South Side?. Suppose $00 is invested for years. Plan pays.% interest compounded daily ( days a year). Plan B pays.% interest compounded quarterly. If the investment is untouched for the entire time, which plan will earn more interest? Eplain your reasoning. 7

5 7- See pages 7-7 for objectives. Skills Objective C In, give the first four terms of the geometric sequence described.. constant ratio, first term -. constant ratio -., first term. first term, second term. g n 0( ) n, for n. g - g n g n for all integers n In 9, a sequence is given. a. Tell if the sequence is geometric. b. If yes, give its constant ratio..,, 08,,... 7.,, 9,,,... a. b. a. b. 8..,., 0.,.,... 9.,,,,... a. b. a. b. 9 7 In 0 and, a geometic sequence is given. a. Give an eplicit formula for the nth term of the sequence. b. Give a recursive formula for the sequence. 0. 0,,.,.0,... a. b.., -.,., -.08,... a. b.. Find the sith term of the geometric sequence whose first term is 7 and whose constant ratio is.. Uses Objective H. car was sold for $,000. If its value decreases % each year, what will be its value after years?. fter each bounce, a ball bounces to 80% of its previous height. If it is originally dropped from a height of feet, how high will it bounce after it hits the floor the th time? 7

6 7- See pages 7-7 for objectives. Skills Objectives, B, and D In, write as a decimal or a simple fraction (.0) Estimate to the nearest integer. In 8, solve. 8. z 9. -y C 7 0. r In and, show that the given number is an eighth root of,.. i. - In and, use the Number of Real Roots Theorem to give the number of real roots possible.. th root(s) of -. 7th root(s) of 8 In 9, write <,, or > in the blank to make the statement true ( ). 0. The equation P N P 0 ( ) n describes the depreciation value of a car over n years, where P N is the price of the car now, P 0 is the original price paid, and is the yearly depreciation rate. If a car costs $, today and cost $,000 four months ago, find the yearly depreciation rate. 7

7 7-7 See pages 7-7 for objectives. Skills Objectives, B, and D In 9, write as a decimal or a simple fraction. Give decimal answers to the nearest hundredth ( ) (0.09) In 0, simplify. 0. y y. z z. ( a b ) In, solve.. y. 8 7 z. k. z In 7 and 8, write <,, or > in the blank to make the statement true If a >, a a. 8. If 0 < b <, b b. 9. Show that -7i is not a fifth root of,807. In 0 and, use the following information: In 9, Johannes Kepler discovered that the average distance d of a planet from the sun and the planet s period of revolution r around the sun are related by the formula 9 d kr. When d is in millions of miles and r is in days, k Mercury, the planet closest to the sun, orbits the sun every 88 days. bout how far is Mercury from the sun?. Neptune is about 79 million miles from the sun. a. Estimate Neptune s period of revolution in days. 7 b. Estimate Neptune s period of revolution in years.

8 7-8 See pages 7-7 for objectives. Skills Objective In, write as a decimal or a simple fraction. Give decimal answers to the nearest hundredth ( ) Skills Objective B In 7 and 8, simplify, using only positive eponents. - 7 y (m n ) y Skills Objective D In 9, solve. 9. y - 0. w - 9. v -. p Suppose >. rrange the following from least to greatest: -,,, -.. True or false. If 0 < k <, then k - > k.. Suppose the formula N 0,000 ( ) -, where t is the time in months and N is the number of items sold per month, models the predicted decline in sales of a specific item over the net months. Will the company sell,000 items months from now? Eplain your reasoning. 9 t 7