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.

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.
• 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 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

The expression (r . s) (a) represents the total number of heartbeats in a lifetime of a person who is a years old. This is because the function r(a) represents the heart rate of a person at a certain age in beats per minute, and the function s(a) represents the total lifespan of a person in minutes. By multiplying r(a) by s(a), we get the total number of heartbeats in a person's lifetime.