Math Problem Statement

  1. Life Expectancy Versus Health Care Spending One article shows a relationship between per capita health care spending h, in thousands of U.S. dollars per person per year, and life expectancy E, in years.39 The following formula is adapted from that article: E=72.23 plus 3.85h minus 0.37h exponent 2. We should point out that this article includes no justification for the type of model used. a. Plot the graph of E versus h. Include spending levels from $1000 to $9000 per person per year (so a horizontal span of 1 to 9).

Solution

Here is the plot of life expectancy EE versus healthcare spending hh in thousands of dollars per person per year. It shows the relationship over a spending range of $1000 to $9000 per person annually.

Would you like to explore more details or have any questions?

Here are 5 questions to consider based on this graph:

  1. How does life expectancy change as healthcare spending increases beyond $9,000?
  2. What does the negative term −0.37h2-0.37h^2 suggest about the relationship between healthcare spending and life expectancy?
  3. Can the model be extrapolated to spending levels beyond the given range?
  4. How does the peak life expectancy in this model compare to real-world data for various countries?
  5. Could other factors, such as socioeconomic status, be influencing the results?

Tip: The quadratic term in the model introduces a diminishing return effect, meaning that after a certain point, additional healthcare spending yields smaller increases in life expectancy.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Data Modeling

Formulas

E = 72.23 + 3.85h - 0.37h^2

Theorems

Quadratic Function Behavior
Vertex of a Parabola
Diminishing Returns

Suitable Grade Level

Grades 10-12

Related Recommendation

Estimating Out-of-Pocket Healthcare Spending Using Exponential Growth

National Health Care Spending Analysis with Exponential Model (1970-2010)

National Health Care Expenditures: Power and Quadratic Models

Predicting Life Expectancy Using Linear Regression Models

Exponential Regression Model for Life Expectancy in the United States (1970-2005)