Functions, Domain, Independent/Dependent

Question

The annual cost of health insurance H as a function of age a is given by the function H(a)=22.6a-119.2 for 15 is less than or equal to a is less than or equal to 90.

What are the independent and dependent variables?

What is the implied domain of the linear function?

What is the health insurance cost for a 30 year old?

What is the age of an individual whose health insurance premium is $1304.60?

Answer 1

*The independent variable is age and the dependent variable is the annual cost of health insurance.

*The domain as given in the problem, was for ages between 15 and 90 (including 15 and 90).

*To find the health insurance cost for a 30 year old, let a=30 and evaluate the expression:

H(a) = 22.6a - 119.2

H(30) = 22.6 * 30 - 119.2

H(30) = 558.8

The annual health insurance cost for a 30 year old is $558.80.

*To find the age of an individual whose annual health insurance cost is $1304.60, let H(a) = 1304.6 and solve for a:

H(a) = 22.6a - 119.2

1304.6 = 22.6a - 119.2

1423.8 = 22.6a

63 = a

63 is the age of an individual with an annual health insurance premium of $1304.60.