Question 1194627: I'm stuck in this exercise can anyone help me please?
Here is the exercise
Caffeine Intake
The half-life of a substance is the amount of time for half of the substance to be eliminated
from the body. Imagine your breakfast has a 16-ounce cup of coffee, a Cool-Mint Chocolate Clif Bar and an apple at 8:00 am.
Part 1: Gather Data
Research the half-life of caffeine. Considering your breakfast, research how much caffeine you
actually consumed and record this total. Be sure to site your (credible) sources and organize the
data you will need to complete Parts 2 and 3.
Part 2: Find your Equation
Find an exponential equation for your data. Clearly state your steps/ process/calculations.
Identify what each part (variables and constants) represents in the equation. Be sure to
identify the specific time for t=0.
2.
Does your model represent a growth or decay situation? Explain how you can tell from the
equation. What does this mean in the context of the problem?
3. Explain, using the context of the problem, why this situation is modeled by an exponential
function instead of a linear function.
4.
How can this equation be used to predict the amount of caffeine in your body at a specific
point in time? Explain in detail and provide an example.
5.
How can this equation be used to predict when then there will be a specific amount of
caffeine in your body? Explain in detail and provide an example.
Part 3: Graph the Data
Graph your equation. Be sure that your graph includes a title, labels, correct scale and at least
accurate points. You may want to create a table of values before graphing the function.
1.
What is the y-intercept of your graph and what does it mean in the context of the problen
2.
What is the x-intercept of your graph and what does it mean in the context of the problem
3.
Use formal limit notation to describe the end behavior of the graph.
4.
How would your graph change if the half-life decreased (takes longer to leave the body)?
5.
One morning you wake up late and instead of having breakfast at 8:00 am, you must wail
until 10:00am. How would this change be represented in your graph? How would your
equation change?
Part 4: Analysis Questions
1. Identify a realistic domain. Explain your reasoning.
2. Identify a realistic range. Explain your reasoning.
3.
Predict the population of caffeine in your body after 8 hours. Explain or show how you
found your answer.
4.
After how long will here be less than 20 mg of caffeine in your body? Show your solution
algebraically and graphically.
5.
Assuming there was no other caffeine in your system prior to your breakfast, what is the
maximum amount of caffeine in your body and at what time does this occur? How is this
value represented in your equation and graph?
6.
When will there be no caffeine in your body (0 mg)? How is this value represented in your
equation and graph?
7.
When is the amount of caffeine decreasing the fastest? Justify your answer mathematically.
8.
Caffeine pills are marketed as an alternative to coffee. One extra strength pill has 250 mg of
caffeine per pill, and a special time release composition that allows it to be released into the
body at a continuous rate. It is recommended that you do not take another dosage until the
amount of caffeine in your system is below 40% of the initial dose. If you take one extra-
strength pill at 8:00 am, at what time would you be able to take another one?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
This problem is on exponential decay.
Similar processes are radioactive decay; a medications decay in a human's body;
eliminating medications from a human body.
To see many other solved similar problems on exponential decay, look into the lessons
- Radioactive decay problems
- A medication decay in a human's body
- Miscellaneous problems on exponential growth/decay (*)
in this site.
Find there many similar solved problems and learn the subject from there.
The most closest to your are the problems 3 and 4 of the lesson marked (*) in the list.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Consider these lessons as your handbook, textbook, guide, tutorials, and (free of charge) home teacher.
Learn the subject from there once and for all.
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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