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 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
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

Answer 1

To find out what \((r \cdot s)(a)\) represents, we need to combine the two functions \(r(a)\) and \(s(a)\) and analyze what they mean.

1. \(r(a) = 211 - 0.64a\) represents the heart rate in beats per minute for a person of age \(a\) years.
2. \(s(a) = 525,600a\) represents the lifespan in minutes of a person who is \(a\) years old (since there are 525,600 minutes in a year, this function essentially calculates the total number of minutes a person lives based on their age in years).

When we multiply \(r(a)\) and \(s(a)\):
\[
(r \cdot s)(a) = r(a) \cdot s(a) = (211 - 0.64a) \cdot (525,600a)
\]
This expression gives us the total number of heartbeats a person has in their lifetime, based on their age \(a\) (in years).

So, the correct interpretation of \((r \cdot s)(a)\) is:
**the total number of heartbeats in a lifetime of a person who is \(a\) years old.**