To understand what \((r \cdot s)(a)\) represents, we first need to analyze the functions \(r(a)\) and \(s(a)\).
- The function \(r(a) = 211 - 0.64a\) represents the heart rate (in beats per minute) of a person who is \(a\) years old.
- The function \(s(a) = 525,600a\) represents the lifespan (in minutes) of a person who is \(a\) years old, based on the total number of minutes in a year (365 days).
Now, when we compute the product \((r \cdot s)(a)\), we are effectively multiplying the heart rate (in beats per minute) by the lifespan (in minutes). This gives us the total number of heartbeats over a lifetime for a person who is \(a\) years old.
Thus, \((r \cdot s)(a)\) represents:
the total number of heartbeats in a lifetime of a person who is \(a\) years old.