Algebra 2B Unit 2 Exam
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Primavera - Online *
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Course
2B
Subject
Mathematics
Date
Nov 24, 2024
Type
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2
Uploaded by Bre6426
Solve the equation for x.
2^4x−3=2^x+18
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x=7
Solve the equation for x.
3^6x+7=243
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x=−1/3
Solve the equation for x.
5
⋅
10^x+2=5,000
Which answer shows the correct steps for solving the equation?
●
x=1
Solve the equation for x.
4
⋅
3^x−2=60
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x=log_3 15 + 2
Match each logarithm with its equivalent expression.
log4^m == m log 4
log_m 15^4 == 4 log_m 15
ln 4^15 == 15 ln 4
What is the value of log_4 62?
●
2.977
If 3x/5=24, what is the value of x?
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x≈14.464
Solve the equation for x.
5^4x−1=845
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x=1.297
Solve 7^2x−9=441 for x.
Which answer shows the correct steps?
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x≈6.065
Cara tracked the population of fish in a pond. At the end of the first year, she counted 8 fish. Over the years, the population
tripled each year.
Which equation can be used to determine the number of fish, f, after t years?
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f=8
⋅
3^(t−1)
The town of Swanford has a population of 12,500, but it is decreasing at a rate of 4% each year.
Which equation models the population of Swanford, where p is the population after t years?
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p = 12,500(0.96)^t
A sample of bacteria is grown in a petri dish. It contains 1,000 bacteria, and the population doubles every half hour. The
inequality 1,000(2)^2t > 50,000, where t is the number of hours, models when the population of the bacteria sample will be
greater than 50,000.
Based on the inequality, when will the population in the sample be greater than 50,000?
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t > 3 hours
Carbon dating is used to determine the age of fossils. A fossil was found with 75% of the original carbon-14. The half-life of
carbon-14 is 5,730 years. The equation that models the situation is 0.75 = (0.5)^ x/5,730.
How old is the fossil?
●
x = 2,378
Examine the graph of the logarithmic function f(x).
https://assets.learnosity.com/organisations/625/bce6b31f-2f50-4523-bbea-71b3a6a7599f.png
Match each part with its value.
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x-intercept of f(x) : (1, 0)
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vertical asymptote of f(x) : x = 0
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intersection of f(x) and the line y = 1 : (0.75, 1)
Examine the following logarithmic function f(x): f(x) = log x. Match each part with its value.
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x-intercept of f(x) : (1, 0)
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vertical asymptote of f(x) : x = 0
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intersection of f(x) and the line y = 1 : (10, 1)
Which interval represents all of the x-values where f(x) = log_13 x is positive?
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0 < x < 1
Examine the following function:
h(x) = log_5 x
Which graph represents the function?
●
https://assets.learnosity.com/organisations/625/96797c9e-4f5f-4cf2-97df-408aaaec87c0.png
The function f(x) = log_3/4 x − 2 is translated to get g(x) = log_3/4 x + 4. What is the effect on f(x)?
●
f(x) moves 6 units upward.
The function f(x) is transformed to become g(x) = f(−2x). Which statement correctly describes the transformation
on f(x)?
●
f(x) is reflected across the y-axis and horizontally compressed by a factor of 1/2.
The graph shows a translation of the preimage f(x) = log_3 x − 2 to become g(x). Which is the transformation rule
and the function rule for g(x)?
■
g(x) = f(x + 2) + 3
■
g(x) = log_3 (x + 2) + 1
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