## Questions and Answers

Which equation can be used to find the number of weeks, x, after which the balance of the fund will reach 1,280?

5(2)^x = 1,280

How many weeks will it take to reach the class goal of $1,280?

x = 8

The value of Sam's car after one year is represented by 17,930(0.81)^x.

False

Which expressions are equivalent to log10(20x^5) - 1?

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Match each logarithmic equation to its corresponding x-value:

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What value of x satisfies the equation 1.5(4)^(2x) = 12?

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What is the approximate solution to the equation 4ln(x) - 8 = 12?

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What is the equation of the transformed function g in terms of f(x) = e^x?

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What is the range of function g if g(x) = -2f(x) + 1?

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The graph of function f has a range of {y| -infinity < x < infinity}.

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Match each transformation of function f with a feature of the transformed function:

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What is the explicit function that describes the sequence 16, 24, 36, 54...?

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Select all functions that can be used to find the number of miles Natalie drives in a month.

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What is the total profit Jessica earned in 5 years?

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Match each series with the equivalent series written in sigma notation:

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What does the function h(x) look like?

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Function g is continuous.

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What should Ronald do with the functions regarding the height of the chest?

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Which expression is equal to f(x) * g(x)?

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As x approaches positive infinity, f(x) approaches ___ and g(x) approaches ___.

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What did Jane record about her marigold sapling?

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What is the approximate value for the solution to the equation f(x) = g(x)?

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Using a table of values, what is the approximate solution to the equation f(x) = g(x) to the nearest quarter of a unit?

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To keep producing a specific shirt style, the company must make a profit of at least $5,000.

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What are the two equations that represent Leo's savings plans?

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Which statements are true about the measure of angle 0 being 7x/4?

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If cos(0) = -3/10 and 0 is in quadrant II, what is the value of tan(0)?

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When a graph is symmetric about the origin, it is an ___ function.

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When a graph is symmetric about the y-axis, it is an ___ function.

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A function is considered even if f(-x) = f(x).

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A function is considered odd if f(-x) = -f(x).

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What is true about the function y=1/2cos(2x)-1?

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To create function d, what transformations occur?

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Which equation matches the function shown in the graph?

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How long does it take for a friend in the left seat to move upward and back to the initial position?

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What function could represent the price tag's height relative to the table top after t seconds?

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What is the sample mean number of trees per block if there must be at least 18 trees?

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Which statement is true about the survey of coffee and tea preferences?

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What is the difference between the experimental probability and the theoretical probability in tire manufacturing?

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If a soccer team wins 65% of matches, how many matches is it expected to lose out of 20?

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What generalization can be made from the results of the grocery store study?

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What kind of statistical study did Thad conduct when evaluating window cleaners?

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Complete the missing values in the table and statement about positive and negative results below.

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Which of the following situations are fair?

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What is the mean midday temperature recorded in June in a city in Southern California?

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Summarize the normal distribution of tomatoes sold weekly by a grocery store.

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The standard error of the mean of the sample is ____ hours.

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By the central limit theorem, which interval can the branch manager be 95% certain that the sample mean will fall within?

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What is the 90% confidence interval for the true proportion of club members who use compost?

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What is the margin of error assuming a 95% confidence level in the restaurant's server study?

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Which statements are true about the marketing department's fabrics?

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What factor is most relevant when evaluating the report from the technology research group on game development?

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## Study Notes

### Fundraising and Exponential Growth

- Ms. Walker's class aims to raise $1,280, starting with a $5 deposit.
- Weekly, the fund doubles, modeled by the equation 5(2)^x = 1,280; it takes 8 weeks to reach the goal.

### Depreciation of Assets

- Sam's car, valued at $17,930, depreciates at 19% annually.

### Logarithmic Expressions

- Equivalent expressions: log10(20x^5) - 1 simplifies to log10(10x).

### Logarithmic Equations and Their Values

- Corresponding values for logarithmic equations:
- log5x=4 → x = 625
- log4x=2 → x = 16
- log10x=3 → x = 1,000
- log2x=5 → x = 32

### Solving Equations

- Solve 1.5(4)^2x = 12 to find x ≈ 0.75.
- Approximate solution for 4Inx - 8 = 12: x ≈ 148.4.

### Transformations of Exponential Functions

- Transformed function g(x) = 3f(x) where f(x) is the parent exponential function f(x) = e^x.
- For g(x) = -2f(x) + 1 derived from f(x) = 10^x, the range is (-∞, 1).

### Characteristics of Function Graphs

- Function f has a range of all real numbers and decreases as x approaches 0.
- Transformations of f(x) = ln x provide varying features, such as vertical asymptote and intercept changes.

### Sequence Representation

- Explicit form of the sequence 16, 24, 36, 54 is f(n) = 16(3/2)^(n - 1).

### Planning and Profit Analysis

- Natalie drives approximately 900 miles each month, starting at 800 miles.
- Jessica's five-year total profit calculation remains unclear, initially posing a profit of $3,125 in the first year.

### Sigma Notation

- Conversions to sigma notation for series:
- 3 + 12 + 48 + 192 + 768 → 3(4)
- 4 + 32 + 256 + 2,048 + 16,384 → 4(8)

### Graphical Transformations and Functions

- Midline for function y = 1/2cos(2x) - 1 is at y = -1.
- Graph transformations include shifts and frequency adjustments.

### Angles and Trigonometry

- Angle 0 = 7x/4 gives tan(0) = -1, with the reference angle being 45°.
- For cos(0) = -3/10 in quadrant II, tan(0) value equals -√91/3.

### Probability and Statistics

- Function g exhibits continuity, with limits approaching positive infinity as x increases.
- A factory's tire molding machine has a 0.2% failure rate, with actual faults at a 0.4% difference from theoretical.

### Sampling and Confidence Intervals

- A sample of 1,000 students reveals a 59% preference for coffee; the population proportion may differ.
- The city council mandates at least 18 trees per block, averaging 21.3 trees, ensuring environmental standards.

### Effectiveness of Products

- Analysis concludes Fabric B as more durable than Fabric A based on double rub ratings, affirming its medium-duty classification.

### Experimental Studies

- Thad conducted an experiment to compare window cleaners by washing half the windows with each brand, demonstrating a practical study approach.

### Growth Measurement in Gardening

- Jane's marigold sapling grows at an increasing rate with decreasing average change over time.

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## Description

This quiz includes practice flashcards for Ms. Walker's Algebra 2B class. It focuses on exponential growth and solving equations related to a fundraising scenario. Test your understanding of functions and their applications in real-world problems.