Algebra: Unit 6

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Unit 6 - Item 1
The function above is an exponential function with an asymptote at 2. Which function below has the same end behavior as x approaches negative infinity?

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Unit 6 - Item 2
A new cell phone model is released, and the number of units sold increases exponentially over time. The function S(t) = 500(1.2)^t models the number of cell phones sold t months after the release.

Unit 6 - Item 2
A new cell phone model is released, and the number of units sold increases exponentially over time. The function S(t) = 500(1.2)^t models the number of cell phones sold t months after the release.

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How many cell phones are sold after 3 months?

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Explain what S(0) represents in this context.

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The company would like to know how the phones are doing within the first year after the release. Sketch the graph of the function ranging from 0 to 12 months.

What is the domain and range of the function based on the first year after the release? (Round to the nearest whole number)

Unit 6 - Item 3
Tina and Karen were doing their homework together. They are trying to compare the ranges of 𝑓(𝑥) = 1 − 2𝑥 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 − 1.

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Complete the table below.

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Sketch a graph of both functions

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Compare the ranges of both functions

Unit 6 - Item 4

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Who is correct? Explain

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Research 5 banking institutions to see what the annual interest rate is today for a savings account. Simulate $4000 and $4500 at each institution for 20 years to see which institution would be the best to invest your money

Unit 6 - Item 5
Imagine a small company that sells an innovative product online. The company tracks the number of units sold each month and uses this data to forecast future sales. The initial sales data shows an exponential growth pattern. The company uses the function 𝑆(𝑡) = 2𝑡 to model the number of units sold 𝑡 months after the product launch.

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Sketch the initial model: 𝑆(𝑡) = 2^𝑡.

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The company wants to analyze how different marketing strategies could affect their sales.

How is the initial model 𝑆(𝑡) = 2𝑡 affected by each of the strategies. Be sure to describe what happens to the graph.

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To understand the broader market trends, the company also compares their sales growth with two other trends below. Compare the initial value, type of function, general shapes of the graphs, and determine which of the additional trends produces more units.

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Unit 6 - Item 6
Given the following function of 𝑓(𝑥) = −32 + 𝑘, what will happen to the graph if you substitute
negatives versus positives for “𝑘”? Explain.

Unit 6 - Item 7
A population of bacteria in a petri dish is modeled by the exponential function below where 𝑡 is time in hours: 𝑷(𝒕) = 𝟓𝟎𝟎(𝟏. 𝟐𝟎)𝒕

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What is the population of the bacteria initially when the bacteria is placed in the petri dish?
Explain.

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Unit 6 - Item 1The function above is an exponential function with an asymptote at 2. Which function below has the same end behavior as x approaches negative infinity?

Unit 6 - Item 2A new cell phone model is released, and the number of units sold increases exponentially over time. The function S(t) = 500(1.2)^t models the number of cell phones sold t months after the release.

How many cell phones are sold after 3 months?

Explain what S(0) represents in this context.

The company would like to know how the phones are doing within the first year after the release. Sketch the graph of the function ranging from 0 to 12 months.What is the domain and range of the function based on the first year after the release? (Round to the nearest whole number)

Complete the table below.

Sketch a graph of both functions

Compare the ranges of both functions

Who is correct? Explain

Research 5 banking institutions to see what the annual interest rate is today for a savings account. Simulate $4000 and $4500 at each institution for 20 years to see which institution would be the best to invest your money

Sketch the initial model: 𝑆(𝑡) = 2^𝑡.

The company wants to analyze how different marketing strategies could affect their sales.How is the initial model 𝑆(𝑡) = 2𝑡 affected by each of the strategies. Be sure to describe what happens to the graph.

To understand the broader market trends, the company also compares their sales growth with two other trends below. Compare the initial value, type of function, general shapes of the graphs, and determine which of the additional trends produces more units.

Unit 6 - Item 6Given the following function of 𝑓(𝑥) = −32 + 𝑘, what will happen to the graph if you substitutenegatives versus positives for “𝑘”? Explain.

What is the population of the bacteria initially when the bacteria is placed in the petri dish?Explain.

Is the bacteria increasing over time or decreasing over time. Explain.

Unit 6 - Item 1
The function above is an exponential function with an asymptote at 2. Which function below has the same end behavior as x approaches negative infinity?

Unit 6 - Item 2
A new cell phone model is released, and the number of units sold increases exponentially over time. The function S(t) = 500(1.2)^t models the number of cell phones sold t months after the release.

The company would like to know how the phones are doing within the first year after the release. Sketch the graph of the function ranging from 0 to 12 months.

What is the domain and range of the function based on the first year after the release? (Round to the nearest whole number)

The company wants to analyze how different marketing strategies could affect their sales.

How is the initial model 𝑆(𝑡) = 2𝑡 affected by each of the strategies. Be sure to describe what happens to the graph.

Unit 6 - Item 6
Given the following function of 𝑓(𝑥) = −32 + 𝑘, what will happen to the graph if you substitute
negatives versus positives for “𝑘”? Explain.

What is the population of the bacteria initially when the bacteria is placed in the petri dish?
Explain.