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Advanced Algebra - Unit 2

Last updated 9 months ago
24 questions
Unit 2 – Item 1

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

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

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

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

  • Click the graph tab.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
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Verify algebraically that f^-1(x) is the inverse of f(x) and g^-1(x)

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Unit 1 – Item 8
Consider the functions 𝑓(𝑥) = 2𝑥^2 and 𝑔(𝑥) = 𝑙o𝑔₂(𝑥)
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PART A
Graph both functions on the same set of axes for the domain 0 < x < 5.

  • Click the graph tab.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
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PART B
Determine the domain and range of each function

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PART C
Identify any points of intersection between the graphs

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

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

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

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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
where M(t) is the mass of the substance at time 𝑡𝑡 in years.
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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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PART C
Algebraically, find the time (𝑡) it takes for the population to reach 3000 bacteria.

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

  • Click the graph tab.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
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