Question
The heart rate of a person can be modeled by the function r(a)=211−0.64a
𝑟
(
𝑎
)
=
211
−
0.64
𝑎
where a
𝑎
is the person's age in years and r(a)
𝑟
(
𝑎
)
is heartbeats per minute. The life span in minutes of a person is modeled by the function s(a)=525,600a
𝑠
(
𝑎
)
=
525
,
600
𝑎
.
Explain what (r⋅s)(a)
(
𝑟
⋅
𝑠
)
(
𝑎
)
represents.
(1 point)
Responses
the total number of heartbeats in a lifetime of a person who is a
𝑎
minutes old
the total number of heartbeats in a lifetime of a person who is A minutes old
the heart rate of a person who is a
𝑎
minutes old
the heart rate of a person who is A minutes old
the heart rate of a person who is a
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
𝑎
years old
𝑟
(
𝑎
)
=
211
−
0.64
𝑎
where a
𝑎
is the person's age in years and r(a)
𝑟
(
𝑎
)
is heartbeats per minute. The life span in minutes of a person is modeled by the function s(a)=525,600a
𝑠
(
𝑎
)
=
525
,
600
𝑎
.
Explain what (r⋅s)(a)
(
𝑟
⋅
𝑠
)
(
𝑎
)
represents.
(1 point)
Responses
the total number of heartbeats in a lifetime of a person who is a
𝑎
minutes old
the total number of heartbeats in a lifetime of a person who is A minutes old
the heart rate of a person who is a
𝑎
minutes old
the heart rate of a person who is A minutes old
the heart rate of a person who is a
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
𝑎
years old
Answers
Answered by
GPT-4o mini
To understand what \((r \cdot s)(a)\) represents, we need to analyze the two functions given:
1. \( r(a) = 211 - 0.64a \) represents the heart rate (in beats per minute) of a person based on their age \( a \) in years.
2. \( s(a) = 525,600a \) represents the life span (in minutes) of a person based on their age \( a \) in years.
When we calculate \((r \cdot s)(a)\), we are effectively multiplying the heart rate \( r(a) \) by the life span \( s(a) \).
\[
(r \cdot s)(a) = r(a) \cdot s(a) = (211 - 0.64a)(525,600a)
\]
The result of this multiplication gives us the total number of heartbeats over the lifetime of a person who is \( a \) years old.
Therefore, 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.**
1. \( r(a) = 211 - 0.64a \) represents the heart rate (in beats per minute) of a person based on their age \( a \) in years.
2. \( s(a) = 525,600a \) represents the life span (in minutes) of a person based on their age \( a \) in years.
When we calculate \((r \cdot s)(a)\), we are effectively multiplying the heart rate \( r(a) \) by the life span \( s(a) \).
\[
(r \cdot s)(a) = r(a) \cdot s(a) = (211 - 0.64a)(525,600a)
\]
The result of this multiplication gives us the total number of heartbeats over the lifetime of a person who is \( a \) years old.
Therefore, 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.**
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