To determine the hourly rate of change of the medicine concentration, we need to analyze the given function:

$C_{\text{minute}}(t) = 61 \cdot (0.96)^t,$ where $t$ is in minutes.

Step 1: Express hourly decay

Since there are $60$ minutes in an hour, we replace $t = 60$ in the function to compute the decay factor for an hour.

The decay factor for $1$ hour is:

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

Step 2: Calculate $(0.96)^{60}$

Using a calculator:

$(0.96)^{60} \approx 0.08693.$

Step 3: Interpret the decay factor

This result means that every hour, the concentration of the medicine in the bloodstream decays by a factor of approximately:

$\boxed{0.09}.$

Thus, the medicine concentration decays by about 91% every hour, leaving only 9% of its concentration.

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Related Questions:

1. How long will it take for the concentration to decay to half of its initial value?
2. What is the initial concentration of the medicine?
3. How can we compute the concentration at $t = 30$ minutes?
4. If the medicine decays by $91\%$ every hour, how much is left after $3$ hours?
5. What happens to the concentration as $t \to \infty$?

Tip:

When dealing with exponential decay, always check whether the given rate is per unit of time (e.g., minute, hour, etc.), and adjust the calculations accordingly!