Warm-up and HW Quiz
Warm-up and HW Quiz
Warm-up and HW Quiz
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SECTION 3.1<br />
WARM-UP EXERCISES<br />
Simplify the expression.<br />
1. 5 2x (5 –x ) 2. 47x<br />
4 3x 3. (23x ) 2 4.<br />
⎛<br />
⎜<br />
⎝<br />
4 x<br />
5 x<br />
⎞<br />
⎟<br />
⎠<br />
−1<br />
DAILY HOMEWORK QUIZ<br />
Evaluate the function at the given value. Round to three decimal places.<br />
1. f (x) = 2 x when x = 1.5 2. f (x) = e −0.5x when x = 4<br />
Graph the function.<br />
3. f (x) = 3 x + 2 4. f (x) = e x−1<br />
5. A total of $5000 is deposited into a savings account earning 4% annual interest<br />
compounded quarterly. Find the balance in the account after 2 years.<br />
ANSWERS<br />
WU 1. 5 x 2. 4 4x 3. 2 6x 4.<br />
QUIZ 1. 2.828 2. 0.135<br />
3. 4.<br />
5 x<br />
4 x<br />
5. $5414.28<br />
26<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.
SECTION 3.2<br />
WARM-UP EXERCISES<br />
Evaluate the expression.<br />
1. 3 3<br />
2. 16 1/2<br />
3. 5 0<br />
4.<br />
⎛ 1⎞<br />
⎝<br />
⎜<br />
2⎠<br />
⎟<br />
−3<br />
5. 81 –1/4<br />
DAILY HOMEWORK QUIZ<br />
1<br />
1. Write the logarithmic equation log 2<br />
=−4 in exponential form.<br />
16<br />
2. Write the exponential equation e 5 = 148.4131... in logarithmic form.<br />
Find the domain, x-intercept, <strong>and</strong> vertical asymptote of the function, <strong>and</strong> sketch its<br />
graph.<br />
3. f (x) = log 2<br />
(x + 1) − 2<br />
4. f (x) = ln x − 1<br />
5. Evaluate f (0.5) for f (x) = log x.<br />
6. Solve ln (x + 4) = ln 10 .<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.<br />
27
ANSWERS<br />
WU 1. 27 2. 4 3. 1<br />
4. 8 5.<br />
1<br />
3<br />
QUIZ 1. 2 −4 = 1<br />
16<br />
2. ln 148.4131... = 5<br />
3. Domain: (−1, ∞) ; x-intercept: (3,0); vertical asymptote: x =−1<br />
4. Domain: (0, ∞); x-intercept: (e, 0) ; vertical asymptote: x = 0<br />
5. −0.30103<br />
6. x = 6<br />
28<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.
SECTION 3.3<br />
WARM-UP EXERCISES<br />
Evaluate the expression.<br />
1. log 7<br />
49 2. log 0.001<br />
3. ln 1<br />
e 2 4. log 16 2<br />
Simplify the expression.<br />
5. 3 2 (3 x ) 6.<br />
5 x<br />
5 y<br />
DAILY HOMEWORK QUIZ<br />
1. Evaluate log 6<br />
40 using the change-of-base formula.<br />
2. Find the exact value of log 8<br />
2 −4 .<br />
3. Exp<strong>and</strong> the expression ln 2x<br />
y 3 .<br />
4. Condense the expression 1 2<br />
log x − log (x + 1) to the logarithm of a single quantity.<br />
ANSWERS<br />
WU 1. 2 2. –3 3. –2<br />
4.<br />
1<br />
4<br />
5. 3 2 + x 6. 5 x – y<br />
QUIZ 1. 2.05880 2. − 4 3<br />
3. ln 2 + ln x − 3 ln y<br />
4. log<br />
x<br />
x + 1<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.<br />
29
SECTION 3.4<br />
WARM-UP EXERCISES<br />
Simplify the expression.<br />
1. log 100 x<br />
2. ln e 4 x<br />
Solve for x.<br />
1. 2x 2 – 3x + 1 = 0<br />
2. x ln 2 = ln 3<br />
3. 4xe = 8e 2<br />
DAILY HOMEWORK QUIZ<br />
1. Determine whether x = 14 is a solution of the equation log 3<br />
(x − 5) = 2.<br />
Solve the equation. Round the result to three decimal places.<br />
2. 43 ( 1−2t<br />
)= 32<br />
3. e 2x + 2e x − 15 = 0<br />
4. 3 + 2 ln x = 8<br />
5. log (x + 5) + log (x − 1) = log (2x + 3)<br />
6. An amount of $1500 is invested in an account at 4.25% compounded continuously.<br />
Find the time required for the amount to triple.<br />
ANSWERS<br />
WU 1. 2x 2. 4x 3.<br />
4. ln 3<br />
ln 2<br />
5. 2e<br />
1<br />
2 , 1<br />
QUIZ 1. yes 2. x ≈ −0.446 3. x ≈ 1.099<br />
4. x ≈ 12.182 5. x = 2 6. 25.8 years<br />
30<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.
SECTION 3.5<br />
WARM-UP EXERCISES<br />
Solve the equation for x. Round the result to three decimal places.<br />
1. 3e 2x = 7<br />
2. 4 –x/2 = 0.12<br />
3. 2 log 2x = 3<br />
4. ln (x + 1) – ln x = 1<br />
DAILY HOMEWORK QUIZ<br />
1. Radioactive radium has a half-life of 1599 years. The quantity Q of radium present<br />
t /1599<br />
⎛ 1⎞<br />
after t years is Q = Q 0<br />
⎝<br />
⎜<br />
2⎠<br />
⎟ , where Q0 is the initial amount present. How long<br />
will it take 30 grams of radioactive radium to decay to 0.5 grams?<br />
2. On the Richter scale the magnitude R of an earthquake of intensity I is given by<br />
R = log I<br />
I 0<br />
, where l 0<br />
= 1 is the minimum intensity used for comparison. Find the<br />
intensity per unit of area for an earthquake with a magnitude of 7.1.<br />
ANSWERS<br />
WU 1. 0.424 2. 3.059 3. 15.811 4. 0.582<br />
QUIZ 1. It takes about 9445 years.<br />
2. The intensity is approximately 12,600,000.<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.<br />
31
SECTION 3.6<br />
WARM-UP EXERCISES<br />
1. Write an equation of the line that passes through (2, 9) <strong>and</strong> (7, 4).<br />
2. Write an equation of the quadratic function with vertex (8, 3) that passes through<br />
the point (12, –21).<br />
Use the graph of f to describe the transformation that yields the graph of g.<br />
3. f(x) = 2 x ; g(x) = 4 − 2 x<br />
4. f(x) = log 2<br />
x ; g(x) = 1+ log 2<br />
(x − 5)<br />
DAILY HOMEWORK QUIZ<br />
Which model best fits the data in the scatter plot?<br />
1. 2.<br />
3. Find a power model for the data.<br />
(1, 3), (2, 7), (3, 12), (4, 18), (5, 23)<br />
4. Find an exponential model for the data.<br />
(2, 75), (3, 104), (4, 130), (6, 180), (9, 249)<br />
32<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.
ANSWERS<br />
WU 1. y = –x + 11 2. y = − 3 2 (x − 8)2 + 3<br />
3. reflection in the x-axis <strong>and</strong> <strong>up</strong>ward shift 4 units<br />
4. <strong>up</strong>ward shift 1 unit <strong>and</strong> right shift 5 units<br />
QUIZ 1. logistic 2. quadratic 3. y = 2.96x 1.3<br />
4. y = 43(0.8) x<br />
Precalculus with Limits: A Graphing Approach 5e, <strong>Warm</strong>-Up Exercises <strong>and</strong> Daily Homework <strong>Quiz</strong> Transparencies<br />
Copyright © Houghton Mifflin Company. All rights reserved.<br />
33
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