This is A 2H.
Name___________________________________
Knowledge Carnival 2 Practice
House________________
(Philly) Phil in the (Billy) Blanks. (1 Point Each)
1) I know that arithmetic sequences and series have a common ___________, whereas geometric difference; ratio
sequences and series have a common ____________.
()
x
1
x
models exponential ___________, whereas f ( x) = 5 models
4
exponential ____________.
decay; growth
3) I know that log 5 125 is really asking the question ______ to what power is ______.
5; 125
4) I know that "log base e of x" is commonly written as ______.
lnx
2) I know that f ( x) =
Evaluate each series. (2 Points)
6
5)
Σ 2n
n=1
42
Determine if the sequence is arithmetic or geometric. Then, find the term named in the
problem. (3 Points Each)
6) 40, 50, 60, 70, ...
Find a32
7) 4, 12, 36, 108, ...
Find a12
Common Difference: d = 10
a32 = 350
Common Ratio: r = 3
a12 = 708588
Explicit: an = 30 + 10n
Explicit: an = 4 ⋅ 3
-1-
n−1
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Worksheet by Kuta Software LLC
Evaluate each series described. (2 Points Each)
8) 1 + 2 + 4 + 8..., n = 6
9) 44 + 54 + 64 + 74..., n = 8
63
632
Evaluate each expression. (2 Points)
10) log 6
1
216
−3
Use a calculator to approximate each to the nearest thousandth. (2 Points)
11) log 3 8
1.893
Solve each equation. Round your answers to the nearest thousandth. (3 Points Each)
12) 19
x + 10
+ 1 = 37
13) 9 ⋅ 10
−8.783
10a + 8
+ 6 = 65
−0.7183
-2-
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Worksheet by Kuta Software LLC
Expand each logarithm. (2 Points)
()
4 5
a
14) log
b
20 log a − 5 log b
Condense each expression to a single logarithm. (2 Points)
15) 5 log 7 u + 6 log 7 v
log 7 (v u
)
6 5
Solve each equation. (3 Points Each)
16) log 11 (4m + 4) = log 11 (5m − 8)
17) log 6 ( p − 5) + 9 = 13
{12}
{1301}
Find the inverse of each function. (2 Points Each)
18) y = log 4 (2x)
x
19) y = 4 + 6
y = log 4 ( x − 6)
x
4
y=
2
-3-
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Worksheet by Kuta Software LLC
Sketch the graph of each function and list its domain and range. (3 Points)
20) y = ln ( x + 2) − 2
y
8
6
4
2
−8
−6
−4
−2
2
4
6
8 x
−2
−4
−6
−8
Poor LeBron... (2 Points)
21) LeBron's hairline recedes at a constant rate of 2% per week. Assuming he currently has a full
head of hair (lol), what percentage of his hair be left a year from now?
Approx 35% Hint: the rate is negative and use A(t) = Pe
rt
Depreciation (2 Points)
22) This year, you buy a car for $40,000 that decreases in value by 11% each year. If you want to sell
the car when it’s worth $15,000, how many year will pass before you have to sell the car? Round
to the nearest year.
Approx. 8 years. Hint: rate is negative and use A(t) = P(a + r)
-4-
t
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Worksheet by Kuta Software LLC