Compute the slope using $m = \dfrac{\text{change in }C}{\text{change in }t} = \dfrac{C_2 - C_1}{t_2 - t_1}$ with the two points you identified.

Once you know the slope, use point-slope form $C(t) - C_1 = m(t - t_1)$ with one of the given points to write an equation for $C(t)$.

After you have the equation for $C(t)$, plug in $C(t)=0$ and solve the resulting equation for $t$ to find the time.

In Desmos, type an expression for the concentration using the two data points and the slope formula directly, for example: C(t) = 37 + (16-37)/(12-5)*(t-5) Desmos will automatically simplify the slope and draw the line.

In a new line, type C(t) = 0 or simply y = 0 to draw a horizontal line representing zero concentration.

Use the intersection tool (or tap/click where the line for C(t) crosses y = 0). The $t$-coordinate (the x-value) of this intersection point is the time, in minutes, when the concentration reaches zero. Read that value from Desmos.

The concentration $C(t)$ decreases linearly with time $t$. The two measurements give you two points on the graph of $C$:

• At $t=5$, $C=37$, so one point is $(5,37)$.
• At $t=12$, $C=16$, so the other point is $(12,16)$.

A linear function is determined by its slope and one point (or by two points).

Use the slope formula with the two points $(5,37)$ and $(12,16)$:

So the concentration is decreasing at a rate of $3$ milligrams per liter per minute.

Use point-slope form with point $(5,37)$ and slope $m=-3$:

Now simplify this to slope-intercept form:

This equation models the concentration at any time $t$ (in minutes).

We want the time when the concentration reaches $0$, so set $C(t)=0$ in the equation and solve for $t$:

Add $3t$ to both sides:

Now divide both sides by $3$:

So, the concentration reaches $0$ milligrams per liter after about $17.33$ minutes from the start of the experiment (answer choice B).