Section: Math 1 Summative Lab Activity | Intro to Algebra & Trigonometry | NextGenU.org
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Students mustViewStart discussions: 1
In this final activity, you will investigate the effect of one of the anabolic steroid drugs that the given equation models. This activity is compartmentalized into four parts.
Step 1. Study
Study the given case problem below.
Step 2. AnalyzeBased on the case problem, you will analyze four parts. Analyze the background information for each part and respond to what is required accordingly.
Part A
- The effect equation given above is a quadratic equation. Use the quadratic formula to solve the equation for t. We take only the positive solution because we cannot have a negative value for time. What is your positive value for t?
- What does this time value represent?
Part B
Background
The rate of change of a function with respect to a variable is called the derivative of the function. If the function is denoted f(x), then its derivative is denoted
Rule 1. The derivative of any constant is zero.
Example:
Rule 2. The derivative of a term with a coefficient and a variable to the power of 1 is the coefficient.
Example:
Rule 3 (The Power Rule). To find the derivative of a term with a power of the variable that is higher than 1, we multiply the coefficient by the power and reduce the power by 1 as
Example:
Example: Find the derivative of the polynomial function
Part C
Fill out the table below by calculating the value of S(t) for each given t.
Graph a rough representation of the effect curve for this function.
Hint:
Positive parabolas are shaped like a smile(red curve), while a function that has a negative sign in front of its first term has a graph that is a negative parabola, and it will be upturning, like a scowl (blue curve).
Positive Parabola Negative Parabola
Part D
Background
The derivative can be used to obtain much information about the function (that is one of the main topics of calculus). By making the derivative equal to zero and solving for t, we can determine how much time after injecting the drug will be of maximum effect in the system.
Example:
This tells us that the drug will be at its strongest in the blood approximately 0.67 hours after it is injected into the bloodstream.
Step 3. Respond
Respond by providing the answer for Parts A-D. Show your complete solutions, and principles used to address what is required for each part. Present your work in an organized manner by part.
Step 4. Share
To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).
Step 5: Interact
To complete the activity, you will need to reply to at least two posts made by your peers in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”
OPTIONAL Step 6: Interact (10 minutes)
If you would like to, you can reply to your peers' posts in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to forum.”
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