As $t$ increases by 1 minute, how much does $V(t)$ increase? Look at the part of the equation that is multiplied by $t$.

In a linear equation of the form $y=mx+b$, $m$ is the slope, or rate of change. In $V(t)=45t+200$, what is playing the role of $m$, and what does that tell you about how the water volume changes each minute?

In Desmos, type V(t) = 45t + 200 (or use y1 = 45x + 200 if you prefer x instead of t). This will graph the volume of water as a function of time.

In a new line, type V(0) (or y1(0) if you used y1). Observe the value Desmos shows; this is the starting volume of water in the tank when the pumping begins.

Now type V(1) - V(0) (or y1(1) - y1(0)). The output is the amount the volume increases when time increases by 1 minute. Interpret this number in terms of liters and minutes to decide which choice best describes the meaning of the coefficient in the model.

A linear function can be written as $y=mx+b$, where:

• $m$ is the slope (rate of change), and
• $b$ is the initial value (the value when the input is 0).

In this problem, the model is $V(t)=45t+200$, so:

• $V$ plays the role of $y$ (volume of water),
• $t$ plays the role of $x$ (time in minutes),
• $45$ is like $m$ (slope), and
• $200$ is like $b$ (initial value).

To find the initial amount of water in the tank, set $t=0$:

So the tank initially contained 200 liters of water. That means 45 cannot represent the initial amount in the tank.

The slope $m$ in a linear model tells how much the output changes when the input increases by 1.

Here, if time increases by 1 minute (from $t$ to $t+1$), the change in volume is:

We will interpret what this value represents in context in the next step.

We found that 45 tells how many liters of water are added each minute, not the initial amount, not the tank's capacity, and not a time.

The choice that matches this interpretation is:

Water is being added at a rate of 45 liters per minute.