To graph the relationship between the battery's capacity and time, we first need to define the variables:

• Let $t$ represent time in minutes.
• Let $C(t)$ represent the battery's capacity at time $t$ (in percentage, %).

Given:

• Initially, the battery has 20% of its full capacity, so $C(0) = 20\%$.
• Every minute, the battery gains an additional 5% of its capacity. Thus, the rate of change of the battery's capacity is 5% per minute.

We can model the battery's capacity as a linear function because the increase is constant every minute. The function can be written as:

$C(t) = 20 + 5t$

Where:

• $C(t)$ is the battery's capacity at time $t$,
• $20$ is the initial capacity (20%),
• $5t$ represents the 5% increase per minute.

Now, we need to consider the domain:

• The battery can never exceed 100% capacity, so we need to find when $C(t)$ reaches 100%.

Setting $C(t) = 100$:

$100 = 20 + 5t$ $5t = 80$ $t = 16$

So, after 16 minutes, the battery will be fully charged (100%).

Graph:

• The x-axis will represent time $t$ in minutes.
• The y-axis will represent the battery capacity $C(t)$ in percent.
• The line will start at $(0, 20)$ and increase linearly by 5% every minute until it reaches $(16, 100)$.

The graph will be a straight line from $(0, 20)$ to $(16, 100)$, with a slope of 5.

Would you like me to create the graph for you?