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 kife span in minutes of a person is modeled by the function s (a) = 525, 600a. explain what (r*s) (a) represents.

Answer 1

The expression \((r * s)(a)\) represents the total number of heartbeats a person will have over their lifetime, based on their age \(a\).

Let's break it down:

1. Heart Rate Function \(r(a)\): The function \(r(a) = 211 - 0.64a\) gives the heart rate in beats per minute as a function of age \(a\). This means that as a person ages, their heart rate decreases linearly.

2. Lifespan Function \(s(a)\): The function \(s(a) = 525,600a\) models the lifespan in minutes for a person of age \(a\). This is calculated based on the assumption that there are 525,600 minutes in a year (60 minutes per hour × 24 hours per day × 365 days per year).

3. Product \((r * s)(a)\): The product \(r(a) * s(a) = (211 - 0.64a)(525,600a)\) multiplies the heart rate by the lifespan.

   • Conceptually, this product gives you the total number of heartbeats that a person will have throughout their lifetime. It calculates how many beats occur per minute (heart rate) and multiplies it by the total number of minutes the person lives (lifespan).

   • Thus, the result of this product represents the total heartbeats across the entire lifespan, providing insight into how the heart functions over a person's life and how it might change as age increases.