Question

The heart rate of a person can be modeled by the function r(a)=211−0.64a
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 (r⋅s)(a)
represents.



(1 point)
Responses

the total number of heartbeats in a lifetime of a person who is a
years 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
minutes old
the heart rate of a person who is A minutes old

the heart rate of a person who is a
years old
the heart rate of a person who is A years old

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

Answer 1

To understand what \((r \cdot s)(a)\) represents, we need to analyze the functions \(r(a)\) and \(s(a)\) given in the problem:

1. \(r(a) = 211 - 0.64a\) represents the heart rate of a person in beats per minute (bpm) based on their age \(a\) in years.
2. \(s(a) = 525,600a\) represents the total lifespan of a person in minutes based on their age \(a\) in years, where \(525,600\) is the number of minutes in a year (60 minutes/hour × 24 hours/day × 365 days/year).

When we multiply these two functions, \((r \cdot s)(a)\), we get:

\[
(r \cdot s)(a) = r(a) \cdot s(a) = (211 - 0.64a) \cdot (525,600a)
\]

This product will give us the total number of heartbeats the person has in their lifetime. Here’s how:

- \(r(a)\) gives us the heart rate in beats per minute.
- \(s(a)\) gives us the total minutes lived by that person at age \(a\).

Thus, multiplying these two gives us the total number of heartbeats completed over the entire lifespan of the person who is \(a\) years old (since it calculates the heartbeats per minute times the total minutes lived).

Therefore, \((r \cdot s)(a)\) represents:

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