To graph a possible function representing the battery charge of a cell phone over the course of a day, we consider the following:

1. Domain: The domain is the time of the day, usually represented from $0$ (midnight) to $24$ hours (end of the day).
2. Range: The range is the battery charge percentage, which varies from $0\%$ (completely drained) to $100\%$ (fully charged).
3. Behavior: The battery charge decreases over time as the phone is used and increases when it is charged. It will typically start high (if fully charged overnight) and fluctuate throughout the day.

Key Features of the Graph

• Starts high (e.g., $100\%$ at midnight).
• Gradual decreases during periods of use.
• Steep increases during charging times.
• Fluctuates based on the phone's activity.

I will create a graph representing this scenario.import matplotlib.pyplot as plt import numpy as np

Time (hours) from 0 to 24

time = np.linspace(0, 24, 500)

Battery charge function (piecewise approximation)

battery_charge = np.piecewise( time, [ (time < 6), # Fully charged overnight (time >= 6) & (time < 10), # Usage in the morning (time >= 10) & (time < 12), # Charging (time >= 12) & (time < 18), # Afternoon usage (time >= 18) & (time < 20), # Charging again (time >= 20) # Evening usage ], [ 100, # Fully charged lambda t: 100 - 20 * (t - 6), # Linear decrease in the morning lambda t: 60 + 40 * (t - 10) / 2, # Charging back up lambda t: 100 - 10 * (t - 12), # Slow decrease in the afternoon lambda t: 40 + 60 * (t - 18) / 2, # Evening charging lambda t: 100 - 30 * (t - 20) # Steep evening usage ] )

Plotting the graph

plt.figure(figsize=(10, 6)) plt.plot(time, battery_charge, label="Battery Charge", color='blue') plt.title("Cell Phone Battery Charge Over One Day", fontsize=14) plt.xlabel("Time of Day (hours)", fontsize=12) plt.ylabel("Battery Charge (%)", fontsize=12) plt.ylim(0, 100) plt.grid(True, which='both', linestyle='--', linewidth=0.5) plt.axhline(0, color='black', linewidth=0.8) plt.axhline(100, color='black', linewidth=0.8) plt.axvline(0, color='black', linewidth=0.8) plt.axvline(24, color='black', linewidth=0.8) plt.legend() plt.show() <<ImageDisplayed>>successHere is a graph that represents a possible function for the battery charge of a cell phone over the course of one day. The battery starts fully charged, decreases during periods of usage, and increases during charging periods. This model illustrates realistic fluctuations in battery charge.

Would you like further explanation or analysis?

Related Questions:

1. What happens if the phone isn't charged at all during the day?
2. How would heavy usage affect the graph's shape?
3. What if the battery depletes completely—how would that be shown?
4. How can we model battery usage for a specific app?
5. What assumptions does this model make about phone usage patterns?

Tip:

When analyzing real-life data like battery life, consider external factors such as screen brightness, app activity, and network connectivity, which can significantly influence usage rates.