Math Problem Statement
The Dangers of Smoking Cigarette smoke con- tains any number of unhealthy substances, cyanide among them. One study modeled cyanide in the bloodstream after smoking a cigarette using
C= 0.1 plus 0.3t exponent 0.6 e exponent -0.17t,
where C is the concentration of cyanide in the bloodstream, measured in nanograms per deciliter, and t is the time, in minutes, since smoking a cigarette.
a. Make a graph of the concentration of cyanide during the first hour after smoking a cigarette. Add the line corresponding to the target level of 0.3 nanogram per deciliter.
Solution
The given function for the concentration of cyanide in the bloodstream is:
Where:
- is the concentration of cyanide in nanograms per deciliter.
- is the time in minutes since smoking a cigarette.
You are tasked with plotting this function for the first hour (i.e., to minutes) and adding a line corresponding to the target concentration of nanograms per deciliter.
Let me generate the plot for you.It seems like I can’t do more advanced data analysis right now. Please try again later.
Would you like to explore the problem further, or have any questions in the meantime?
Here are some related questions:
- What happens to the cyanide concentration after more than 60 minutes?
- How would the model change if the decay rate of cyanide were slower?
- What other substances in cigarette smoke have similar effects on the body?
- How does the half-life of cyanide in the bloodstream affect long-term exposure?
- What is the significance of the target concentration of 0.3 ng/dL?
Tip: Exponential decay models are often used in pharmacokinetics to describe how substances decrease in concentration in the
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Math Problem Analysis
Mathematical Concepts
Exponential Decay
Algebraic Functions
Modeling in Applied Mathematics
Formulas
C(t) = 0.1 + 0.3t^0.6 * e^(-0.17t)
Theorems
Exponential Decay Model
Graphing Functions
Suitable Grade Level
Grades 10-12
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