Question

make an order of magnitude estimate of the following quantity. explain the assumption used in your estimation.
the number of times the average persons heart beats in a day

choose the correct answer below.

a. 432,000; assuming an average persons heart beats 5 times a second
b. 1440; assuming an average persons heart beats once a minute
c. 86,400; assuming an average persons heart beats once a second
d. 8640; assuming an average persons heart beats once every 10 seconds

Explanation:

Step1: Analyze Option A

Heart beats 5 times per second. There are \(60\) seconds in a minute, \(60\) minutes in an hour, and \(24\) hours in a day. So total beats: \(5\times60\times60\times24 = 5\times86400=432000\). But normal heart rate is about 60 - 100 beats per minute, so 5 beats per second (300 beats per minute) is too high.

Step2: Analyze Option B

Heart beats once per minute. Total beats in a day: \(1\times60\times24 = 1440\). Normal heart rate is much higher, so this is incorrect.

Step3: Analyze Option C

Heart beats once per second. So per minute: \(60\) beats, per hour: \(60\times60 = 3600\) beats, per day: \(3600\times24=86400\). Normal resting heart rate is around 60 - 100 beats per minute, which is 1 - 1.67 beats per second. So once per second (60 beats per minute) is a reasonable estimate for order of magnitude.

Step4: Analyze Option D

Heart beats once every 10 seconds. So per minute: \(6\) beats, per hour: \(6\times60 = 360\) beats, per day: \(360\times24 = 8640\). This is too low as normal heart rate is higher.

Answer:

C. 86,400; assuming an average person's heart beats once a second