Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. All rights reserved. Chapter 6 Exponential and Logarithmic Functions

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. findand

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. findand

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. findand the domain of

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. findand the domain of

Slide Copyright © 2009 Pearson Education, Inc. Find the inverse of the function and state its domain and range. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the inverse of the function and state its domain and range. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Graph the function as a solid curve and its inverse as a dashed curve. a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph the function as a solid curve and its inverse as a dashed curve. a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. The function is one-to-one. Find its inverse. a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. The function is one-to-one. Find its inverse. a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Change to an equivalent expression involving logarithms. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Change to an equivalent expression involving logarithms. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the exact value of a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the exact value of a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Suppose that ln 2 = a and ln 5 = b. Use the properties of logarithms to write ln 10 in terms of a and b. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Suppose that ln 2 = a and ln 5 = b. Use the properties of logarithms to write ln 10 in terms of a and b. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Write as the sum and/or difference of a. b. c. d. logarithms. Express powers as factors.

Slide Copyright © 2009 Pearson Education, Inc. Write as the sum and/or difference of a. b. c. d. logarithms. Express powers as factors.

Slide Copyright © 2009 Pearson Education, Inc. Use the Change-of-Base Formula and a calculator to evaluate a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Use the Change-of-Base Formula and a calculator to evaluate a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Solve the equation a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Use a graphing utility to solve the equation a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Use a graphing utility to solve the equation a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Austin invested $12,000 in an account at 11% compounded quarterly. Find the amount in Austin’s account after a period of 6 years. a.$11, b.$23, c.$22, d.$22,395.63

Slide Copyright © 2009 Pearson Education, Inc. Austin invested $12,000 in an account at 11% compounded quarterly. Find the amount in Austin’s account after a period of 6 years. a.$11, b.$23, c.$22, d.$22,395.63

Slide Copyright © 2009 Pearson Education, Inc. A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. a.3.44% b.3.40% c.3.04% d.36%

Slide Copyright © 2009 Pearson Education, Inc. A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. a.3.44% b.3.40% c.3.04% d.36%

Slide Copyright © 2009 Pearson Education, Inc. What principal invested 8% compounded continuously for 4 years will yield $1190? a.$ b.$ c.$ d.$864.12

Slide Copyright © 2009 Pearson Education, Inc. What principal invested 8% compounded continuously for 4 years will yield $1190? a.$ b.$ c.$ d.$864.12

Slide Copyright © 2009 Pearson Education, Inc. Gillian has $10,000 to invest in a mutual fund. Using average annual rate of return for the past five years of 12.25%, determine how long it will take for her investment to double. a.6 years b.12 years c.3 years d.4 years

Slide Copyright © 2009 Pearson Education, Inc. Gillian has $10,000 to invest in a mutual fund. Using average annual rate of return for the past five years of 12.25%, determine how long it will take for her investment to double. a.6 years b.12 years c.3 years d.4 years

Slide Copyright © 2009 Pearson Education, Inc. The size P of a small herbivore population at time t (in years) obeys the function P(t) = 600e 0.14t if they have enough food and the predator population stays constant. After how many years will the population reach 1200? a.4.95 years b years c years d.12.8 years

Slide Copyright © 2009 Pearson Education, Inc. The size P of a small herbivore population at time t (in years) obeys the function P(t) = 600e 0.14t if they have enough food and the predator population stays constant. After how many years will the population reach 1200? a.4.95 years b years c years d.12.8 years

Slide Copyright © 2009 Pearson Education, Inc. The half-life of silicon-32 is 710 years. If 20 grams is present now, how much will be present in 400 years? a b c d.0

Slide Copyright © 2009 Pearson Education, Inc. The half-life of silicon-32 is 710 years. If 20 grams is present now, how much will be present in 400 years? a b c d.0

Slide Copyright © 2009 Pearson Education, Inc. A thermometer reading 93ºF is placed inside a cold storage room with a constant temperature of 36ºF. If the thermometer reads 88ºF in 14 minutes, how long before it reaches 54ºF? Use Newton’s Law of Cooling: U = T + (U 0 – T)e kt. a.–37 min b.176 min c.–2 min d.40 min

Slide Copyright © 2009 Pearson Education, Inc. A thermometer reading 93ºF is placed inside a cold storage room with a constant temperature of 36ºF. If the thermometer reads 88ºF in 14 minutes, how long before it reaches 54ºF? Use Newton’s Law of Cooling: U = T + (U 0 – T)e kt. a.–37 min b.176 min c.–2 min d.40 min

Slide Copyright © 2009 Pearson Education, Inc. The logistic growth function a.600 butterflies b.343 butterflies c.360 butterflies d.7200 butterflies describes the population of a species of butterflies t months after they are introduced to a non- threatening habitat. How many butterflies are expected in the habitat after 20 months?

Slide Copyright © 2009 Pearson Education, Inc. The logistic growth function a.600 butterflies b.343 butterflies c.360 butterflies d.7200 butterflies describes the population of a species of butterflies t months after they are introduced to a non- threatening habitat. How many butterflies are expected in the habitat after 20 months?

Slide Copyright © 2009 Pearson Education, Inc. A mechanic is testing the cooling system of a boat engine. He measures the engine’s temperature over time. Use a graphing utility to build a logistic model from the data. a. c. b. d. Time, min Temperature, ºF

Slide Copyright © 2009 Pearson Education, Inc. A mechanic is testing the cooling system of a boat engine. He measures the engine’s temperature over time. Use a graphing utility to build a logistic model from the data. a. c. b. d. Time, min Temperature, ºF