Final answer:
The heart rate is calculated by doubling the number of beats counted in 30 seconds, yielding 80 beats per minute. The uncertainty is determined using the propagation of uncertainty formula and rounds to ±2 bpm, resulting in a heart rate and uncertainty of 80 ± 2 bpm.
Step-by-step explanation:
To calculate the heart rate and its uncertainty in beats per minute (bpm), we use the measurement of 40 ± 1 beats in 30.0 ± 0.5 seconds. To find the heart rate in bpm, we double the number of beats counted in 30 seconds:
Heart rate = (Number of beats / Time in seconds) × 60 seconds/minute
Heart rate = (40 beats / 30 seconds) × 60 seconds/minute = 80 beats/minute
Now we need to calculate the uncertainty. The uncertainty in the heart rate can be found using the formula for the propagation of uncertainty:
± (∇Heart rate) = Heart rate × ( ± (∇Number of beats) / Number of beats + ± (∇Time) / Time )
± (∇Heart rate) = 80 beats/minute × ( ± 1 beat / 40 beats + ± 0.5 seconds / 30 seconds )
± (∇Heart rate) = 80 beats/minute × ( 0.025 + 0.0167 ) = 80 beats/minute × 0.0417 ≈ 3.3 bpm
After rounding to the nearest whole number, the uncertainty is ±2 bpm.
Therefore, the heart rate is 80 ± 2 bpm, which corresponds to option b) 80 ± 2 bpm.