Advanced Algebra - Unit 2

Last updated about 1 year ago

24 Nsɛmmisa

Advanced Algebra - Unit 2

Last updated about 1 year ago

24 Nsɛmmisa

Unit 2 – Item 1

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Unit 1 – Item 8

Consider the functions 𝑓(𝑥) = 2𝑥^2 and 𝑔(𝑥) = 𝑙o𝑔₂(𝑥)

DOK 3

AA.FGR.3.1

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Unit 2 - Item 3

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If the initial population
is 1,000 bacteria. Find the population funtion.

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PART B
Determine the time it takes for the population to double.

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PART C
After 10 hours, the population is measured to be 2500 bacteria. Calculate the initial population

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Unit 2 - Item 4

A sample of a radioactive substance has an initial mass of 150 grams. The substance

decays exponentially over time according to the equation

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where M(t) is the mass of the substance at time 𝑡𝑡 in years.

Part A
Determine the half life of the substance

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Part B
After 15 years, find the remaining mass of the substance

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PART C
If the remaining mass of the substance is 75 grams, calculate the time it took for this amount to decay.

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Unit 2 - Item 5

The population of a city is modeled by the exponential growth function 𝑃(𝑡) = 5000∙1.04^𝑡, where 𝑃(𝑡) is the population at time 𝑡 in years.

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PART A
Determine the annual growth rate of the city's population

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PART B
After how many years will the population reach 10,000 residents?

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PART C
If the population of the city is projected to triple, find the time it will take for this to happen.

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Unit 2 – Item 8

The population of a species of bacteria is modeled by the exponential growth function

𝑃(𝑡) = 500∙ 1.2^𝑡, where 𝑃(𝑡) is the population at time in hours.

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PART A
Create a table to represent the population of bacteria for 𝑡 = 0, 1, 2, 3, 4 hours.

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PART B
Use the exponential equation to calculate the population at 𝑡 = 5 hours

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Advanced Algebra - Unit 2

Advanced Algebra - Unit 2

If the initial population is 1,000 bacteria. Find the population funtion.

PART BDetermine the time it takes for the population to double.

PART CAfter 10 hours, the population is measured to be 2500 bacteria. Calculate the initial population

Part ADetermine the half life of the substance

Part BAfter 15 years, find the remaining mass of the substance

PART CIf the remaining mass of the substance is 75 grams, calculate the time it took for this amount to decay.

PART ADetermine the annual growth rate of the city's population

PART BAfter how many years will the population reach 10,000 residents?

PART CIf the population of the city is projected to triple, find the time it will take for this to happen.

PART ACreate a table to represent the population of bacteria for 𝑡 = 0, 1, 2, 3, 4 hours.

PART BUse the exponential equation to calculate the population at 𝑡 = 5 hours

Part A:Find the inverse of the exponential function f(x) algebraically and express it as f^-1(x)

Part B:Find the inverse of the logarithmic function g(x) algebraically and express it as g^-1(x)

Part CCreate tables to show the values of f(x) and g^−1(x) for x = 1, 2, 3, 4.

Part DGraph the function f(x) and g^-1(x) on the same set of axes, clearly labeling each curve

Verify algebraically that f^-1(x) is the inverse of f(x) and g^-1(x)

PART AGraph both functions on the same set of axes for the domain 0 < x < 5.

PART BDetermine the domain and range of each function

PART CIdentify any points of intersection between the graphs

PART DDiscuss the behavior of each function as x approaches positive infinity

PART ECompare and contrast the growth rates of f(x) and g(x) based on their graphs andbehavior.

If the initial population is 1,000 bacteria. Find the population funtion.

PART BDetermine the time it takes for the population to double.

PART CAfter 10 hours, the population is measured to be 2500 bacteria. Calculate the initial population

Part DIf the population reaches 4,000 bacteria, find the time it takes for the population to be reached

Part ADetermine the half life of the substance

Part BAfter 15 years, find the remaining mass of the substance

PART CIf the remaining mass of the substance is 75 grams, calculate the time it took for this amount to decay.

PART ADetermine the annual growth rate of the city's population

PART BAfter how many years will the population reach 10,000 residents?

PART CIf the population of the city is projected to triple, find the time it will take for this to happen.

PART ACreate a table to represent the population of bacteria for 𝑡 = 0, 1, 2, 3, 4 hours.

PART BUse the exponential equation to calculate the population at 𝑡 = 5 hours

PART CAlgebraically, find the time (𝑡) it takes for the population to reach 3000 bacteria.

PART DGraph the exponential function and analyze the behavior of the population over time

Part A:Find the inverse of the exponential function f(x) algebraically and express it as f^-1(x)

Part B:Find the inverse of the logarithmic function g(x) algebraically and express it as g^-1(x)

Part CCreate tables to show the values of f(x) and g^−1(x) for x = 1, 2, 3, 4.

Part DGraph the function f(x) and g^-1(x) on the same set of axes, clearly labeling each curve

Verify algebraically that f^-1(x) is the inverse of f(x) and g^-1(x)

PART AGraph both functions on the same set of axes for the domain 0 < x < 5.

PART BDetermine the domain and range of each function

PART CIdentify any points of intersection between the graphs

PART DDiscuss the behavior of each function as x approaches positive infinity

PART ECompare and contrast the growth rates of f(x) and g(x) based on their graphs andbehavior.

Part DIf the population reaches 4,000 bacteria, find the time it takes for the population to be reached

PART CAlgebraically, find the time (𝑡) it takes for the population to reach 3000 bacteria.

PART DGraph the exponential function and analyze the behavior of the population over time

If the initial population
is 1,000 bacteria. Find the population funtion.

PART B
Determine the time it takes for the population to double.

PART C
After 10 hours, the population is measured to be 2500 bacteria. Calculate the initial population

Part A
Determine the half life of the substance

Part B
After 15 years, find the remaining mass of the substance

PART C
If the remaining mass of the substance is 75 grams, calculate the time it took for this amount to decay.

PART A
Determine the annual growth rate of the city's population

PART B
After how many years will the population reach 10,000 residents?

PART C
If the population of the city is projected to triple, find the time it will take for this to happen.

PART A
Create a table to represent the population of bacteria for 𝑡 = 0, 1, 2, 3, 4 hours.

PART B
Use the exponential equation to calculate the population at 𝑡 = 5 hours

Part A:
Find the inverse of the exponential function f(x) algebraically and express it as f^-1(x)

Part B:
Find the inverse of the logarithmic function g(x) algebraically and express it as g^-1(x)

Part C
Create tables to show the values of f(x) and g^−1(x) for x = 1, 2, 3, 4.

Part D
Graph the function f(x) and g^-1(x) on the same set of axes, clearly labeling each curve

PART A
Graph both functions on the same set of axes for the domain 0 < x < 5.

PART B
Determine the domain and range of each function

PART C
Identify any points of intersection between the graphs

PART D
Discuss the behavior of each function as x approaches positive infinity

PART E
Compare and contrast the growth rates of f(x) and g(x) based on their graphs and
behavior.

If the initial population
is 1,000 bacteria. Find the population funtion.

PART B
Determine the time it takes for the population to double.

PART C
After 10 hours, the population is measured to be 2500 bacteria. Calculate the initial population

Part D
If the population reaches 4,000 bacteria, find the time it takes for the population to be reached

Part A
Determine the half life of the substance

Part B
After 15 years, find the remaining mass of the substance

PART C
If the remaining mass of the substance is 75 grams, calculate the time it took for this amount to decay.

PART A
Determine the annual growth rate of the city's population

PART B
After how many years will the population reach 10,000 residents?

PART C
If the population of the city is projected to triple, find the time it will take for this to happen.

PART A
Create a table to represent the population of bacteria for 𝑡 = 0, 1, 2, 3, 4 hours.

PART B
Use the exponential equation to calculate the population at 𝑡 = 5 hours

PART C
Algebraically, find the time (𝑡) it takes for the population to reach 3000 bacteria.

PART D
Graph the exponential function and analyze the behavior of the population over time

Part A:
Find the inverse of the exponential function f(x) algebraically and express it as f^-1(x)

Part B:
Find the inverse of the logarithmic function g(x) algebraically and express it as g^-1(x)

Part C
Create tables to show the values of f(x) and g^−1(x) for x = 1, 2, 3, 4.

Part D
Graph the function f(x) and g^-1(x) on the same set of axes, clearly labeling each curve

PART A
Graph both functions on the same set of axes for the domain 0 < x < 5.

PART B
Determine the domain and range of each function

PART C
Identify any points of intersection between the graphs

PART D
Discuss the behavior of each function as x approaches positive infinity

PART E
Compare and contrast the growth rates of f(x) and g(x) based on their graphs and
behavior.

Part D
If the population reaches 4,000 bacteria, find the time it takes for the population to be reached

PART C
Algebraically, find the time (𝑡) it takes for the population to reach 3000 bacteria.

PART D
Graph the exponential function and analyze the behavior of the population over time