Question

In the above study, the investigators determined that a low concentration of DNP increased the average life span from 719 days (Control) to 770 days (DNP). If the U.S. population has an average life span of 79 years, then how many years would be added if the same percentage increase were observed?

Short answer

If the same percentage increase were observed in the U.S. population as in the study, it would result in an addition of approximately 5.61 years to the average life span.

Step-by-step solution

Calculate the percentage increase in life span

First, we need to calculate the percentage increase in life span between the control group and the DNP group. To do this, we will use the formula: Percentage increase = \(\frac{New \ life \ span - Old \ life \ span}{Old \ life \ span}\) * 100

Apply the percentage increase to the U.S. population's life span

Next, we'll apply the percentage increase calculated in step 1 to the average life span of the U.S. population (79 years). To find how many years would be added to the U.S. population's life span, we'll use the formula: Years added = Original life span (in years) * Percentage increase

Calculate the results

Now, we'll perform the calculations using our given data and formulas. 1. Calculate the percentage increase in life span: Percentage increase = \(\frac{770-719}{719}\) * 100 Percentage increase ≈ 7.1% 2. Apply the percentage increase to the U.S. population's life span: Years added = 79 * 0.071 Years added ≈ 5.61 Therefore, if the same percentage increase were observed in the U.S. population, it would result in an addition of approximately 5.61 years to the average life span.

Key concepts

Percentage Increase

Percentage increase is a useful measure when comparing the change in value of a quantity over time. It is expressed as a percentage of the original or old value. For instance, in comparing the life span of a population before and after the introduction of a substance like DNP, it’s important to quantify how much the life span has changed relative to the original value.

In the exercise, you learn to calculate the percentage increase by finding the difference between the new life span and the old life span, then dividing by the old life span, and finally multiplying by 100. This formula:
\[ \text{Percentage increase} = \left(\frac{\text{New life span} - \text{Old life span}}{\text{Old life span}}\right) \times 100 \]
is crucial to understand because it can be applied to various real-world scenarios, from population studies to finance and economics.

Average Life Span

The average life span, or life expectancy, is the average number of years a population is expected to live. It's an indicator of the overall health and wellness of the population, often influenced by factors such as healthcare, diet, and social conditions.

The average life span also serves as a benchmark to evaluate the effectiveness of dietary supplements or medical interventions, much like in the provided exercise. When we talk about the life span increasing, it implies an improvement in these factors, or the introduction of beneficial agents like DNP in the study. This concept is particularly helpful in population health assessments and can be influenced by genetics, lifestyle, and advancements in healthcare technology.

Population Statistics

Population statistics encompass a range of data points that tell us about the characteristics of a population. These statistics can include information on life span, birth rates, death rates, disease prevalence, and many other factors that affect population health.

In the context of this life span calculation exercise, population statistics would take into consideration the average life span of a specific population, like that of the U.S., to make predictions or assessments on the impact of certain variables. Understanding population statistics can lead to better decision-making in public health and policy, as it allows experts to track changes over time and assess the effectiveness of health interventions.