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 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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