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
represents.

Responses

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

the heart rate of a person who is a years old

1 answer

The function \( s(a) = 525,600a \) represents the total number of minutes in a person's life based on their age in years, since there are 525,600 minutes in a year (60 minutes/hour × 24 hours/day × 365 days/year).

To identify the correct interpretation of the function \( s(a) \):

  • The first option: "the total number of heartbeats in a lifetime of a person who is a years old" is applicable, but needs clarification regarding how heart rates relate to the lifespan.
  • The second option: "the heart rate of a person who is a minutes old" is incorrect as \( s(a) \) relates to years, not minutes.
  • The third option: "the total number of heartbeats in a lifetime of a person who is a minutes old" is incorrect because the function is defined in terms of years.
  • The fourth option: "the heart rate of a person who is a years old" refers to the function \( r(a) \), not \( s(a) \).

Thus, the correct response regarding the function \( s(a) = 525,600a \) is:

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

Remember that to find the total heartbeats, you would need to multiply the heart rate (from \( r(a) \)) by the lifespan in minutes.