It looks like you're dealing with two equations that describe blood pressure as a function of time using sinusoidal functions. Here's how we can interpret and work through them:

1. Equation for Blood Pressure $P$:

$P = 15 \sin(2\pi t) + 110$

This equation represents blood pressure, where:

• $P$ is the blood pressure at time $t$,
• $\sin(2\pi t)$ represents a periodic oscillation with a period of 1 unit of time (since $2\pi$ completes a full cycle every unit of time),
• The amplitude of the oscillation is 15 (indicating how much the pressure fluctuates above and below its average),
• The term $+110$ represents the average or baseline blood pressure (mean value),
• $t$ is time.

2. Equation for Blood Pressure with a modified variable $P^*$:

$P^* = 15 \sin(2\pi t^*) + 110$

This equation seems to be structurally similar to the first one but involves $P^*$, which might be a modified or alternative model for blood pressure based on another time variable $t^*$. The difference between $t$ and $t^*$ could represent a time shift, change in measurement conditions, or something else specific to the problem context.

In general:

• Both equations describe oscillations in blood pressure over time with a mean value of 110 and an amplitude of 15.
• The blood pressure fluctuates periodically, repeating its behavior every unit of time due to the $2\pi t$ term in the sine function.

If you would like to understand further details on how this model works (e.g., period, frequency, amplitude, or phase shifts) or explore the relationship between $t$ and $t^*$, feel free to ask!

Questions for further exploration:

1. What is the period of oscillation for this blood pressure model?
2. How would the graph of $P$ look over time? Can we sketch or visualize it?
3. What does the amplitude of 15 signify in a medical context?
4. How would a phase shift affect the blood pressure model?
5. What does the difference between $t$ and $t^*$ represent physically?

Tip: The sine function is periodic, meaning it repeats its values in a regular cycle. Understanding the period and amplitude can help interpret the behavior of systems modeled by sine functions.