what is the minimum rate of consumption in gallons per day

To find the minimum rate of gasoline consumption in gallons per day, we need to determine where the graph has the smallest slope since the slope of the graph represents the rate of consumption.

### Analyzing the Graph

- The graph shows the amount of gasoline in the tank over time. The rate of consumption corresponds to the steepness of the graph, where a steeper slope indicates a higher rate of consumption, and a less steep (flatter) slope indicates a lower rate of consumption.
  
### Steps to Determine the Minimum Rate of Consumption

1. **Examine the slope at different points on the graph:**
   - Between days 0 and 1: The slope is quite steep, indicating a high rate of consumption.
   - Between days 1 and 2: The slope appears to be less steep than between days 0 and 1.
   - Between days 2 and 4: The slope is even less steep, particularly around day 3, indicating the lowest rate of consumption.
  
2. **Identify the interval with the flattest slope:**
   - Visually, the slope seems the flattest between days 2 and 4, indicating that this is where the rate of consumption is lowest.

3. **Estimate the rate of consumption in this interval:**
   - At day 2, the gasoline level is approximately 9.5 gallons.
   - At day 4, the gasoline level is approximately 8 gallons.
   - Total consumption over 2 days (from day 2 to day 4) is:
     \[
     9.5 \, \text{gallons} - 8 \, \text{gallons} = 1.5 \, \text{gallons}
     \]
   - Average rate of consumption in this interval:
     \[
     \frac{1.5 \, \text{gallons}}{2 \, \text{days}} = 0.75 \, \text{gallons per day}
     \]

### Conclusion

The minimum rate of consumption occurs between days 2 and 4, with an approximate rate of **0.75 gallons per day**.

### Would you like more details or have any other questions?

Here are some related questions you might find interesting:

1. How does the maximum rate of consumption compare to the minimum rate?
2. What factors could cause fluctuations in the rate of consumption?
3. How could you model this data using a piecewise linear function?
4. If the car's fuel efficiency is 20 miles per gallon, how far does it travel at the minimum consumption rate?
5. How might this consumption pattern affect long-term travel planning?

**Tip:** To determine the rate of change (like consumption rates) from a graph, always look at the slope: steep slopes indicate high rates, while flatter slopes indicate lower rates.

Discover how to determine the minimum rate of gasoline consumption in gallons per day using graph analysis. This problem involves understanding the slope of a graph, which represents the rate of consumption over time.

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