The Problem

The linear function given by models the number of radio stations on the air from 1950 to 1995. (Source: National Association of Broadcasters.)  Determine an equation whose solution is the year when there were 10000 radio stations on the air and then solve the equation graphically, symbolically, and numerically.

The number 10000 in this problem represents the value of  . So replacing with 10000 gives us the following equation to solve:

10000 = 214.2 (x – 1950) + 2322


Solving the Equation Symbolically

Solving symbolically means using the normal procedures of algebra to obtain a solution.

214.2 (x – 1950) + 2322 = 10000

214.2 x – 417690 + 2322 = 10000

214.2 x - 415368 = 10000

214.2 x = 425368

x   1985.845

Original Equation

Distributive Property

Combine Like Terms

Add 415368 to Both Sides

Divide Both Sides by 214.2

Thus, according to this model, in 1985 there were approximately 10,000 stations on the air.



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