The given function modeling the concentration of medicine in the bloodstream is:

$C_{\text{minute}}(t) = 61 \cdot (0.96)^t$

Here, $t$ is the time in minutes, and the base $0.96$ represents the decay factor per minute.

To find the decay factor per hour, we need to convert the minute-based decay factor into an hour-based decay factor. Since there are 60 minutes in an hour, we raise the minute-based decay factor to the power of 60:

$\text{Hourly decay factor} = (0.96)^{60}$

Let's calculate this value:

$\text{Hourly decay factor} \approx (0.96)^{60} \approx 0.2825$

So, every hour, the medicine concentration decays by a factor of approximately 0.28 when rounded to two decimal places.

Would you like more details or have any questions?

Here are 5 relative questions to expand your understanding:

1. How would the medicine concentration change after 2 hours?
2. What does the decay factor of 0.28 per hour imply about the medicine's effectiveness?
3. How would the model change if the medicine concentration increased instead of decreased?
4. How could this decay factor be used to determine the best time to administer the next dose?
5. What would be the concentration after 30 minutes?

Tip: Exponential decay models are commonly used in pharmacokinetics to describe how drugs are processed in the body over time. Understanding the decay factor helps in dosing schedules.