P Conol - 4.7 Review, Practice, & CST_ Polynomial and Rational Functions
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Peyton Conol | 11.9.23 - 4.7 Review, Practice, & CST: Polynomial and Rational Functions
Answer the following questions using what you've learned from this unit. Write your responses
in the space provided.
1. Check all correct answers (there may be more than one). (2 points)
In the expression
a
b
,
A.
The value
b
is an exponent.
B.
The value
a
tells you how many times to multiply
b
by itself.
C.
The value
a
must be > 1.
D.
The value
b
tells you how many times to multiply
a
by itself.
E.
The value
b
must be an integer.
2. Simplify the expression below. Write your answer with only positive exponents. (2 points)
(
a
2
b
2
c
a
5
c
2
)(
a
3
b
c
4
)=
b
3
c
5
3. Combine into a single logarithm. (2 points)
3log
(
x
+
y
)+
2log
(
x
−
y
)−
log
(
x
2
+
y
2
)
x
−
y
¿
2
¿
x
+
y
¿
3
⋅
¿
¿
¿
log
¿
4. Use rules of logarithms to expand. (2 points)
x
+
3
¿
2
¿
x
2
+
5
¿
4
¿
(
x
−
2
)
¿
¿
log
¿
5. Rewrite as an exponential equation. (2 points)
ln
(
x
+
y
)=
5
e
5
=
x
+
y
6. Rewrite as a logarithmic equation. (2 points)
2
4
=(
a
−
b
)
lo g
2
(
a
−
b
)=
4
7. Evaluate each expression. (4 points)
a.
lo g
2
32
¿
5
b.
log
(
0.0001
)
¿
−
4
c.
ln
e
−
3
¿
−
3
d.
lo g
4
1
¿
0
8. Evaluate the expression below. Write your answer to three decimal places. (2 points)
lo g
6
95
¿
2.542
9. Solve for
x
. (2 points)
logx
+
log
(
x
−
1
)=
log
(
4
x
)
x
=
5
10. Solve for
x
. Write your answer to three decimal places. (2 points)
1.05
¿
3
x
=
3000
(
1000
)
¿
x
=
7.506
11. Solve for
t
. Write your answer to three decimal places. (2 points)
2500
=
500
e
0.06
t
t
=
26.824
12. Choose the best descriptor for the graph of
f
(
x
) =
ln
(
x
- 5). (2 points)
a.
It increases rapidly, goes through the point (5, 1), then increases gradually.
b.
It increases slowly, goes through the point (5, 1), then increases rapidly.
c.
It increases slowly, goes through the point (6, 0), then increases gradually.
d.
It increases rapidly, goes through the point (6, 0), then increases gradually.
13. Choose the best descriptor for the graph of
f
(
x
) =
e
-
x
+ 5. (2 points)
a.
It increases and goes through the point (0, 6).
b.
It decreases and goes through the point (0, 6).
c.
It increases and goes through the point (5, 1).
d.
It decreases and goes through the point (5, 1).
14. Find the 21st term of the geometric sequence that begins 2, 6, 18, 54, ... (3 points)
3
¿
20
=
6973568802
a
21
=
2
¿
15. Find the sum of the first six terms of the geometric sequence for which
a
2
= 0.7 and
a
3
=
0.49. (3 points)
S
6
=
2.31
16. Rewrite using radicals. (2 points)
a
3
4
¿
5
¿
¿
a
3 4
√
a
3
17. Rewrite using rational exponents. (2 points)
5
√
x
2
¿
x
2
5
18. If you deposit $1,000 into an account that pays 4% interest compounded continuously, how
long will it take the account to grow to $2,000? (3 points)
17.33
years
19. If you pour a cup of coffee that is 200F, and set it on a desk in a room that is 68F, and 10
minutes later is it 145 F, what temperature will it be 15 minutes after you originally poured it? (3
points)
126.8
∘
F
20. Krypton-91 is a radioactive substance that decays very quickly. The function
Q
(
t
)=
Q
0
e
−
kt
models the radioactive decay of krypton-91. Q represents the quantity remaining
after
t
seconds, and the decay constant,
k
, is approximately 0.07. How long will it take a quantity
of krypton-91 to decay to 10% of its original amount? Round your answer to the nearest second.
(3 points)
32.894
seconds ≈
33
seconds
For questions 21 - 23,
complete the statement using the function
f
(
t
)=
L
1
+
Ce
−
bt
:
21. This function is known as a
logarithmic
growth function. (1 point)
22. This function in the previous question is used to model population growth when resources are
limited
. (1 point)
23. In this function,
L
represents the
carrying capacity
of the environment for this population. (1
point)
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