Cellular Service

Question

The model E=-0.475a^2+37.0a-44.6 represents the annual expenditure for cellular service E (in $) for individuals a year old. Use the formula to determine the age(s) at which the average annual expenditure for cellular service is $600. Round the solutions to the nearest year.

Answer 1

Set E = 600 to obtain -0.475a² + 37a - 644.6 = 0

 

By the quadratic formula,

 

a = [-37 ± √((37)² - 4(-0.475)(-644.6))]/(2(-0.475))

 

   = [-37 ± √144.26]/(-0.95)

 

   ≈ 26 or  52

 

The average annual expenditure for cellular service is $600 for 26 year olds and 52 year olds.  

 

 

Answer 2

This problem is an application of the quadratic formula. Start by setting "E" equal to 600 in the given model equation. You now have an equation that can be solved. Subtract 600 from both sides of the equation. 

 

This gives you: -0.475a^2 + 37.0a - 644.6 = 0.

 

Use the quadratic formula to solve for a.

 

Questions?