Question

carmen checks her phone battery throughout the morning.

• at 8:00 a.m., its at 100%
• at 10:00 a.m., its at 80%
• at 11:00 a.m., its at 60%

the graph below shows the battery percentage over time.
questions:

1. how could you describe how fast her battery is draining? is it draining at the same rate each hour?
2. what story does this data tell about carmens phone usage? what does the pattern suggest about her behavior?

Explanation:

Step1: Calculate the rate of battery drain from 8 - 10 am

The time elapsed from 8:00 a.m. to 10:00 a.m. is \(t_1=10 - 8=2\) hours. The battery percentage change is \(\Delta B_1=100 - 80 = 20\%\). The rate \(r_1=\frac{\Delta B_1}{t_1}=\frac{20}{2}=10\%\) per hour.

Step2: Calculate the rate of battery drain from 10 - 11 am

The time elapsed from 10:00 a.m. to 11:00 a.m. is \(t_2=11 - 10 = 1\) hour. The battery percentage change is \(\Delta B_2=80 - 60=20\%\). The rate \(r_2=\frac{\Delta B_2}{t_2}=\frac{20}{1}=20\%\) per hour.

Answer:

1. The battery is not draining at the same rate each hour. From 8 - 10 am, the rate is \(10\%\) per hour, and from 10 - 11 am, the rate is \(20\%\) per hour.
2. The data suggests that Carmen's phone usage increased between 10 - 11 am compared to 8 - 10 am. The steeper slope (higher rate of battery drain) from 10 - 11 am implies more intensive phone use during that hour.