Problem 31 - Calculate With Confidence

Question

A client’s pulse rate decreases from 80 beats per minute to 72 beats per minute. What is the percent of decrease? ____________

Step-by-Step Solution

Answer

The percent decrease in pulse rate is 10%.

Step 1: Determine the decrease in pulse rate

First, we need to find out how much the pulse rate has decreased. To do this, subtract the final pulse rate from the initial pulse rate: Initial pulse rate = 80 beats per minute, Final pulse rate = 72 beats per minute. Decrease in pulse rate = 80 - 72 = 8 beats per minute.

Step 2: Calculate the percent decrease

Now, we need to express this decrease as a percentage of the original pulse rate. The formula to calculate the percent decrease is:\[ \text{Percent decrease} = \left( \frac{\text{Decrease}}{\text{Original amount}} \right) \times 100 \% \]Substitute the values we have:\[ \text{Percent decrease} = \left( \frac{8}{80} \right) \times 100 \% \]

Step 3: Simplify and calculate the percent decrease

Simplify the fraction:\( \frac{8}{80} = \frac{1}{10} = 0.1 \)Now calculate:\[ \text{Percent decrease} = 0.1 \times 100 \% = 10 \% \]

Key Concepts

Pulse Rate Calculation

When determining a percent decrease in pulse rate, it's essential to identify the original and final pulse rates. Pulse rate records the number of heartbeats per minute, serving as an indicator of cardiac health. In our scenario, the pulse rate drops from 80 to 72 beats per minute.
Understanding how much the pulse rate changes is the first task. This means calculating the difference between the initial and final values:

• Initial Pulse Rate: 80 beats/min
• Final Pulse Rate: 72 beats/min

To find the change in pulse rate, simply subtract the final rate from the initial:

• Decrease = 80 - 72 = 8 beats/min

Now, we know the pulse rate has dropped by 8 beats per minute, setting the foundation for percentage calculations.

Mathematical Formulas

Mathematical formulas streamline the calculation process, especially for determining percent changes. For percent decrease, the formula is:

• \[ \text{Percent Decrease} = \left( \frac{\text{Decrease}}{\text{Original Amount}} \right) \times 100 \% \]

This formula helps express any reduction as a percentage of the initial quantity. It's a straightforward way to gauge the significance of a change. For our example, the decrease is 8, and the original pulse rate is 80.

• Substitute the values into the formula:

\[ \text{Percent Decrease} = \left( \frac{8}{80} \right) \times 100 \% \]This setup now ready for simplification below.

Problem-Solving Steps

Grasping the problem-solving process in calculating percent decrease involves finishing the calculation reliably. After substituting the values into the formula, the next step is simplifying the fraction:

• \( \frac{8}{80} = \frac{1}{10} = 0.1 \)

Once simplified, multiply by 100 to convert to a percentage:

• \[ \text{Percent Decrease} = 0.1 \times 100 \% = 10 \% \]

Each step clarifies how a single-digit number in the denominator influences the final answer. Simplifying fractions and setting up the calculation ensures precision.
This distilled understanding of changes via percent forms the backbone of many mathematical evaluations, from finance to biology.