If $s$ is the number of seconds, how many hours is that? Write $h$ in terms of $s$ using the fact that 1 hour equals 3,600 seconds.

After you write $h$ in terms of $s$, substitute that expression into $h/6$ and simplify the fraction in the exponent. Then match the simplified exponent with one of the answer choices.

In Desmos, define a function for the original model using $x$ for hours:

• Type f(x) = 1200*(1/2)^(x/6).

Check that $f(6)$ is 600 to confirm the half-life of 6 hours.

Since $h = s/3600$, define a new function in Desmos using $t$ for seconds:

• Type g(t) = 1200*(1/2)^((t/3600)/6).

Let Desmos simplify the exponent internally; this is the correct model in seconds.

For each answer choice, define a function of $t$ (seconds) in Desmos (for example, A(t) = 1200*(1/2)^(21600*t), B(t) = ..., etc.). Then compare their values to $g(t)$ at a key time, such as $t = 21600$ (which is 6 hours). The choice whose function matches $g(21600)$ (and in general overlaps $g(t)$ on the graph) is the correct equation.

The given model is

The exponent $h/6$ means: after 6 hours ($h=6$), the exponent is 1, so the mass becomes $1{,}200\cdot(1/2)^1 = 600$ milligrams. So the half-life is 6 hours, and $h$ measures time in hours.

We want the model in terms of seconds $s$, not hours $h$.

Use the conversion between hours and seconds:

• 1 hour $= 3600$ seconds.

So if $s$ is the number of seconds, then the number of hours that have passed is

We will substitute this expression for $h$ in the exponent.

Replace $h$ with $s/3600$ in the exponent $h/6$:

So the correct model in terms of seconds $s$ is

which corresponds to answer choice D.