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.

The given function for the concentration of cyanide in the bloodstream is:

\[
C(t) = 0.1 + 0.3t^{0.6} e^{-0.17t}
\]

Where:
- \( C(t) \) is the concentration of cyanide in nanograms per deciliter.
- \( t \) is the time in minutes since smoking a cigarette.

You are tasked with plotting this function for the first hour (i.e., \( t = 0 \) to \( t = 60 \) minutes) and adding a line corresponding to the target concentration of \( 0.3 \) 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:
1. What happens to the cyanide concentration after more than 60 minutes?
2. How would the model change if the decay rate of cyanide were slower?
3. What other substances in cigarette smoke have similar effects on the body?
4. How does the half-life of cyanide in the bloodstream affect long-term exposure?
5. 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

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 + 0.3t^0.6 * e^(-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.

Explore the mathematical modeling of cyanide concentration in the bloodstream after smoking a cigarette. This includes graphing an exponential decay function with the formula C(t) = 0.1 + 0.3t^0.6 * e^(-0.17t), focusing on the first hour after smoking and a target concentration of 0.3 nanograms per deciliter. Ideal for Grades 10-12 students learning about exponential decay and applied mathematics.

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