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Chapter 8: Problem 4

As you might guess, medical-related expenses tend to increase with age. The average annual per capita (per person) expense for health care in America can be modeled by the formula $$E=136 A-1116$$ where \(E\) is the average per capita expense (dollars) associated with a person of age \(A\) ( years). a. Determine the average per capita health care expense for a 30 -year-old person. b. At approximately what age will a person typically incur annual health care expenses of \(\$ 8000 ?\)

Short Answer

Expert verified
Based on the given formula, the average per capita health care expense for a 30-year-old person is $2964. The age at which a person will typically incur annual health care expenses of $8000 is approximately 67 years old.

Step by step solution

01

(Step 1: Understand the given formula and identify the known values)

We are given the formula: $$E=136A-1116$$ where, \(E\) = average per capita expense (dollars), \(A\) = age of the person (years). For question a, we know the age \(A=30\) and we need to find the expense \(E\). For question b, we know the expense \(E=8000\) and we need to find the age \(A\).
02

(Step 2: Calculate the expense for a 30-year-old person)

To find the expense for a 30-year-old person, simply substitute the given age into the formula: $$E = 136(30) - 1116$$ Now compute the equation to find \(E\): $$E = 4080 - 1116$$ $$E = 2964$$ So, the average per capita health care expense for a 30-year-old person is \(\$2964\).
03

(Step 3: Find the age when the annual health care expense is $8000)

To find the age when the expense is $8000, substitute the given expense into the formula: $$8000 = 136A - 1116$$ Now solve the equation for \(A\): $$A = \frac{8000 + 1116}{136}$$ $$A \approx 66.59$$ Since the age must be in whole years, we can round up the age to \(67\) years old. Therefore, a person will typically incur annual health care expenses of \(\$8000\) at approximately \(67\) years old.

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