of s 72. (Modeling) U.S. Radio Stations The graph shows the number on the air, a
ID: 3136901 • Letter: O
Question
of s 72. (Modeling) U.S. Radio Stations The graph shows the number on the air, along with the graph of a linear function that value 2 radio 1 U.S. Radio Stations models the data. 16,000 14,000 12,000 S10,000 8000 E 6000 4000 2000 1950 1960 1970 1980 1990 2000 2010 2020 Year Source: Federal Communications Commission. (a) An equation for a linear model, based on data from 1950-2014 (where x -0 represents 1950,x 10 represents 1960, and so on) is y 200.02x + 2727.7. Determine the slope. (See Example 6.) What does the slope of this line repre sent? Why is the slope positive? (b) Use the model in part (a) to predict the number of stations in 2018.Explanation / Answer
Answer: (a) slope, m=200.02 (b) Number of stations in 2018 is 16329
Explanation:
(a) y=200.02x+2727.7
Comparing this equation with a linear equation, y=mx+c, where, m represents the slope and c=intercept.
So, slope, m=200.02
The slope of the line represents the rate at which the number of radio stations varies with time (years). In other word, with change in every year the number of radio stations are changed by 200.02.
Now, since with the increase in time (years) the number of radio stations also increases. That's why the slope, m=200.02 is positive.
(b) y=200.02x+2727.7
for 2018, x=2018-1950=68. So,
y=200.02*68+2727.7
y=13601.36+2727.7
y=16329.06
y=16329 Radio stations.
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