Mathematics Algebra II Unit 08: Exponential Functions, Equations and Inequalities

Transcription

1 Mathematics Algebra II Unit 08: Exponential Functions, Equations and Inequalities

2 1 Where is the asymptote for the graph of? A x = 0 B y = 0 C y = x D The graph has no asymptotes. 5 The length of time in hours, t, that milk will stay fresh depends on the storage temperature in degrees Celsius, s. Because bacteria grow exponentially, you can assume freshness decays exponentially. The equation below models this situation: t = 146( ) (s 4) 2 y + 5 = b x has moved the parent function y = b x in what way? F vertical translation 5 units up G vertical translation 5 units down H horizontal translation 5 units right J horizontal translation 5 units left How long will milk keep if it is stored at 16 C? A about 36 hours B about 63.6 hours C about 4.1 hours D about 48.2 hours 3 The weight of a particular bacteria in a culture is tripling every hour. The weight of the bacteria was originally 1 grams. 6 Given that b > 0, discuss the differences in the two functions shown below. Include asymptotic behavior, critical points, domain, range, etc. A. Write an equation which expresses the weight, w, in grams, after t, hours. B. Calculate the weight of the bacteria after 2 hours. 4 Suppose that the wealth of a business owner is increasing exponentially. In 1993, he had $40 million. In 2001, he had $55 million. For the domain of 1993 to 2010, what is a reasonable range for this situation? F G $40 million to $28 million $40 million to $5.2 million H $40 million to $20.3 million J $40 million to $8. million Page 2 GO ON

3 Solve: 10 If 3 x + 2 = 2 2, what is the value of x? 8 Solve: 9 a 5 < 29 F a > 5.5 G a < 5.5 H a > 8 J a < 8 9 Merlin Industries bought a laptop for $2,100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar. 11 Which of the following tables of values could be exponential? A x: y: B x: y: C x: y: A $912 B $988 C $1,086 D $4,043 D x: y: Page 3 GO ON

4 12 Sketch the graph of the given function. Then state the function's domain and range. F y = 1.2(3) x G The domain is all real numbers, and the range is all negative numbers. H The domain is all negative numbers, and the range is all real numbers. J The domain is all real numbers, and the range is all positive numbers. The domain is all positive numbers, and the range is all real numbers. Page 4 GO ON

5 13 The percent concentration of poisonous gas in a room is at 45%. An exhaust system is being used to clear the poisonous gas. The exhaust system fans are decreasing the concentration exponentially by 5% each hour. The area cannot be entered when the concentration is above 15%. A. Determine an inequality that could be used to express the number of hours, t, for which the room is safe to enter. B. Solve the inequality on the graph below. C. Verify the solution using a table. Time Concentration Page 5 STOP

6 Test Key Mathematics Algebra II Unit 08: Exponential Functions, Equations and Inequalities ## Item # Correct Answer Primary SE Secondary SE Obj/Cat 1 GEO CS B A2.11(B) 2 GEO20106CS G A2.11(B) 3 GEO CS A. B. 153 grams 4 GEO20101CS J A2.11(C) 5 GEO20098CS B Domain for both is all real numbers. Range for both is y > 0. Both graphs pass through (0,1). 6 MA D A2.11(B) is an increasing function, but the other is decreasing. Both have the x-axis as an asymptote. LOC A2.11(D) 8 GEO20102CS J A2.11(E) 9 LOC20856 B 10 LOC A2.11(D) 11 MA D C 12 A220854CS F A2.11(C) A. 0.45(.95) t <.15 B. t > 21.42

7 13 MA D C. t > Time Concentration