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Algebra 2 7-6 Complete Lesson: Natural Logarithms

Last updated almost 4 years ago
37 questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
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Solve It! A function f is bounded above if there is some number B that f(x) can never exceed. The exponential function base e shown here is not bounded above.

  • Yes
  • No
  • 3
  • 2
  • Not bounded above
  • Is the logarithmic function base e bounded above?
  • If the logarathmic function base e is bounded above, find a bounding number. If not, drag "Not bounded above" into this category.
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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 3 Got It?

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Problem 3 Got It?

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Problem 3 Got It?

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Problem 4 Got It? Space: A spacecraft can attain a stable orbit 300 km above Earth if it reaches a velocity of 7.7 km/s. The formula for a rocket's maximum velocity v in kilometers is shown below.
The booster rocket fires for t seconds and the velocity of the exhaust is c km/s. The ratio of the mass of the rocket filled with fuel to its mass without fuel is R.

  • PART 1: Yes. The maximum firing velocity of 15 km/s is greater than the 7.7 km/s needed for a stable orbit.
  • PART 1: No. The maximum firing velocity of 5.4 km/s is less than the 7.7 km/s needed for a stable orbit.
  • PART 2: Yes. You can increase the mass ratio R, increase the exhaust velocity c, or decrease the firing time t until v > 7.7 km/s.
  • PART 2: No. No matter how the mass ratio R, exhaust velocity c, and firing time t are adjusted, v will remain less than 7.7 km/s.
  • PART 1: A booster rocket for a spacecraft has a mass ratio of about 15, an exhaust velocity of 2.1 km/s, and a firing time of 30 s. Can the spacecraft achieve a stable orbit 300 km above Earth? Explain.
  • PART 2: Reasoning: Suppose a rocket, as designed, cannot provide enough velocity to achieve a stable orbit. Could alterations to the rocket make a stable orbit achievable? Explain.
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Error Analysis: Describe the error made in solving the equation. Then find the correct solution.

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Review Lesson 7-5: Solve the equation. Show your work.

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Review Lesson 7-5: Solve the equation. Show your work.
Enter only a number (the value of x), as an improper fraction.

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Review Lesson 6-7: Find the inverse of the function. Show your work.

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Review Lesson 6-7: Find the inverse of the function. Is the inverse a function?

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Review Lesson 6-7: Find the inverse of the function. Show your work.

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Review Lesson 6-7: Find the inverse of the function. Is the inverse a function?

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Review Lesson 2-2: Given that y varies directly with x, find y in each scenario.

  • y = 5/2
  • y = 3
  • y = 15
  • y = 10
  • y = 4/3
  • y = 6/5
  • If x = 2 when y = 4, find y when x = 5.
  • If x = 1 when y = 5, find y when x = 3.
  • If x = 10 when y = 3, find y when x = 4.
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Vocabulary Review: Categorize each statement as true or false.

  • The function
    and b ≠ 1 is called a logarithmic function.
  • A logarithmic equation is an equation that contains only one logarithm.
  • The logarithm of a power is the difference of the logarithm and the exponent.
  • True
  • False
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Enter only a number.

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Enter only a number.

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Enter only a number.

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Enter only a number.

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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

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Reflection: Math Success