Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 2
2.
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.
3 points
3
Question 3
3.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 4
4.
Take Note: Define the natural logarithmic function.
10 points
10
Question 5
5.
Take Note: Write the numeric value of e to the nearest hundredth.
10 points
10
Question 6
6.
Take Note: Graphing
At desmos.com, graph the parent natural logarithmic function, y=ln, the exponential function y=e^{x}, and y=x on the same plane.
Zoom and pan your graph to establish an appropriate viewing window.
Capture a screenshot of your graph and add it to the Formative canvas.
10 points
10
Question 7
7.
Take Note: The graphs of y=ln \space x and y=e^x are reflexive about the line y=x. What does that indicate about the functions?
10 points
10
Question 8
8.
Problem 1 Got It?
10 points
10
Question 9
9.
Problem 1 Got It?
10 points
10
Question 10
10.
Problem 1 Got It?
3 points
3
Question 11
11.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 12
12.
Problem 2 Got It?
10 points
10
Question 13
13.
Problem 2 Got It?
10 points
10
Question 14
14.
Problem 2 Got It?
3 points
3
Question 15
15.
Video Check: Select all that apply with regards to the video embedded directly above this item.
10 points
10
Question 16
16.
Take Note: Summarize the process of solving a natural log equation that is demonstrated in Problem 3.
10 points
10
Question 17
17.
Problem 3 Got It?
10 points
10
Question 18
18.
Problem 3 Got It?
10 points
10
Question 19
19.
Problem 3 Got It?
3 points
3
Question 20
20.
Video Check: Select all that apply with regards to the video embedded directly above this item.
20 points
20
Question 21
21.
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.
10 points
10
Question 22
22.
🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?
