If $s$ is the number of minutes after the injection, how can you write the time in hours, $t$, using $s$? (Think $t = \text{minutes} / 60$.)

After replacing $t$ with $s/60$ in $C(t)=50e^{-0.07t}+2$, you get an exponent of $-0.07\cdot s/60$. Rewrite $0.07$ as a fraction and simplify $0.07/60$.

Type f(t) = 50*e^(-0.07*t) + 2 into Desmos. This represents the drug concentration when $t$ is in hours.

Type a new expression using minutes: g(s) = 50*e^(-0.07*(s/60)) + 2. This directly applies the relationship $t = s/60$ inside the exponent.

For each answer choice, type its formula as a function of s (or x) in Desmos. For example, h(s) = 50*e^(-7*s/6000) + 2 for one option. Use a table (e.g., test $s=0, 60, 120$) or the graphs to compare outputs of each option to g(s). The correct answer is the one whose graph exactly overlaps g(s) at all points or matches its table values.

The given model is

where $t$ is measured in hours.

If $s$ is the time in minutes after the injection, then the relationship between $t$ and $s$ is:

• $60$ minutes $= 1$ hour, so
• $t$ hours $= s$ minutes means $t = \dfrac{s}{60}$.

We want a formula that uses $s$ instead of $t$.

Replace $t$ with $s/60$ in the original model:

Now the only variable is $s$ (in minutes), but the exponent can be simplified.

Simplify the product $0.07\cdot \dfrac{1}{60}$.

Write $0.07$ as a fraction:

• $0.07 = \dfrac{7}{100}$.

Then

So the exponent becomes $-\dfrac{7}{6000}s$.

Substitute the simplified exponent back into the expression for $C(s)$:

This matches answer choice B, $C(s)=50e^{-\dfrac{7s}{6000}}+2$.