To understand what \( (rs)(a) \) represents, we need to analyze the functions provided:
- The heart rate function \( r(a) = 211 - 0.6a \) gives us the heartbeats per minute based on the person's age \( a \) in years.
- The lifespan function \( s(a) = 525,600a \) provides the total lifespan in minutes based on the person's age \( a \) in years. This function indicates how long a person lives, as there are 525,600 minutes in a year.
Now, \( (rs)(a) \) is the product of the heart rate \( r(a) \) and the lifespan \( s(a) \). This product will yield:
\[ (rs)(a) = r(a) \cdot s(a) = (211 - 0.6a) \cdot (525,600a) \]
This calculation represents the total number of heartbeats throughout a person's lifetime, given their heart rate at age \( a \) and their lifespan in minutes since it calculates the number of heartbeats per minute over a total lifespan measured in minutes.
Therefore, the correct interpretation of \( (rs)(a) \) is:
the total number of heartbeats in a lifetime of a person who is a years old.
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