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.

Here is the graph of the cyanide concentration during the first hour after smoking a cigarette. The blue curve represents the concentration of cyanide over time, while the red dashed line marks the target level of 0.3 nanograms per deciliter.

Do you need further details on how this graph was constructed, or do you have any questions?

### Related Questions:
1. What happens to the cyanide concentration after 60 minutes?
2. How would increasing the rate of decay (-0.17) affect the concentration?
3. What is the significance of the \( t^{0.6} \) term in the model?
4. How does the target level of 0.3 nanograms per deciliter compare to safe exposure levels for cyanide?
5. Could this model be applied to other toxins in cigarette smoke?

### Tip:
Exponential decay models like this one are often used to represent the elimination of substances from the body, such as drugs or toxins.

The Dangers of Smoking Cigarette smoke contains 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. 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 how cyanide concentration in the bloodstream changes after smoking a cigarette, modeled using an exponential decay function. This graph-based problem covers important concepts like mathematical modeling, exponential decay, and target concentration levels, suitable for students in Grades 10-12.

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