https://file.aiquickdraw.com/mathbot/file/1726798420954i0udnc28.jpg

From the given graph, we can deduce the domain and range for the radioactive decay situation.

### Domain:
The domain represents the possible values for the time, \( t \) (in years). Looking at the graph, the time starts at \( t = 0 \) and extends to around \( t = 8 \) years. Since time cannot be negative and is constrained to the provided range, the reasonable domain is:
\[
\text{Domain: } [0, 8] \, \text{years}.
\]

### Range:
The range represents the possible values for the amount of the substance remaining (in grams). From the graph, the amount of substance starts at around 8 grams and asymptotically approaches 0 grams as time increases. Since the amount of substance cannot be negative, the reasonable range is:
\[
\text{Range: } [0, 8] \, \text{grams}.
\]

Would you like to go over any specific aspects or further details on how the domain and range were determined?

Here are 5 follow-up questions to explore:
1. How do you determine the half-life from this graph?
2. How does the exponential decay model relate to this graph?
3. What is the equation for radioactive decay, and how can you derive it using the graph?
4. How does the graph behave as time approaches infinity?
5. How would you calculate the remaining substance after a certain time using the equation?

**Tip:** In problems involving exponential decay, keep in mind that the substance never fully reaches zero—it approaches zero asymptotically.

Find the reasonable domain and range for the given radioactive decay graph.

Determine the reasonable domain and range of a radioactive decay situation using an exponential decay graph. Understand how time and substance amounts change over time. Ideal for high school students learning about decay processes and graph interpretation.

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