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

Question

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 heart rate of a person who is a
minutes old
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 minutes old

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
years old

Answer 1

To understand what \((r \cdot s)(a)\) represents, we first need to analyze the functions \(r(a)\) and \(s(a)\).

1. The function \(r(a) = 211 - 0.64a\) represents the heart rate (in beats per minute) of a person who is \(a\) years old.
2. 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.