Question

The heart rate of a person can be modeled by the function r (a) = 211 - 0.6 where a is the person's age in years and r (a) is heartbeats per minute. The life span in minutes of a person is modeled by the function s(a) = 525, 600a

Explain what (rs)(a) represents.

(1 point)

the heart rate of a person who is a minutes old

the total number of heartbeats in a lifetime of a person who is a minutes old

the total number of heartbeats in a lifetime of a person who is a years old

the heart rate of a person who is a years old

Answer 1

To understand what \( (rs)(a) \) represents, we need to analyze the functions provided:

1. The heart rate function \( r(a) = 211 - 0.6a \) gives us the heartbeats per minute based on the person's age \( a \) in years.
2. 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.**