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e
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300
Decay, r < 0
Is the function growth or decay?
Explain.
0.023x
f (x )  245e
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300
y=0
What is the asymptote of all (non-shifted)
exponential graphs?
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100
Growth, b > 1
Tell whether the function represents
exponential growth or decay. Explain.
2
f (x )   
3
x
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Y = 250000(.88)^x
-200
Approx $131,932.98
A tool and die business purchases a piece
of equipment for $250,000. The value
depreciates at a rate of 12% each year.
Write an exponential decay model for the
value of the equipment. What is the value
after 5 years?
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400
y-int: 1 or (0,1)
asymptote: y = -2
Find the y-intercept and the asymptote of
and graph: y  3x 1  2
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-200
Domain: all real numbers
Range: y >4
Graph the function. Then state the
domain and range of
1
y  
3
 x 2
4
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500
D: all real, R: y > -3,
Y-int: -2, Asymptote: y = -3
Graph the function. List the domain,
range, y-intercept and asymptote.
y  2 3
x
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Dom: x > -1, Range: all real ,
-300
x-int: 0,
asymptote: x = -1
Graph the function. List the domain, range,
x-intercept and asymptote.
y  log6 (x  1)
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Approx 0.2466
100
Evaluate:
e 1.4
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[e^(6x-2)]/4
300
Simplify:
2
e 


 2e 
3x
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400
Approx $829.79
You deposit $725 in an account that pays
4.5% annual interest compounded
continuously. What is the balance after 3
years?
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300
“e” is an irrational number
Explain in your own words what “e” is.
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2
500
Evaluate:
log8 64
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200
9^x =3
Write in exponential form:
log9 3  x
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400
y = 2^x+1
Find the inverse of the function:
f (x )  log2 (x  1)
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-200
Evaluate:
Approx 0.8856
log9 7
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400
Multiplication becomes addition
Division becomes subtraction
Powers get brought out in front of
the word “log”
Explain in your own words how to
expand a logarithm.
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-300
2log( )x+log( )y-log( )z
base2
Expand the log:
base2
base2
x 2y
log2
z
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300
Log((sqrt x)/4)
Condense the log:
1
log x  log 4
2
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-200
Approx 2.54
Approximate:
log1.5 2.8
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1/3
300
Solve:
2
(3x 1)
4
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200
Solve:
Approx 0.258
5 (1x )
9
e
1 
3
2
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400
Solve:
X = 11
log3 (x  2)  5  7
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400
Solve:
X = 1.5
ln(5x  1)  ln(3x  2)
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