The year becomes 1993, when the newspaper circulation is closest to the average circulation.
Part a:
The function is n(x)=0.00792x^3−0.37x^2+3.557x+51.588
The formula for the average of the function is 1b−a∫baf(x)dx
The year 1986 corresponds to 6 and 2000 corresponds to 20 as x is the number of years since 1980.
Obtain the average:
1b−a∫baf(x)dx==≈1/20−6∫20-6[0.00792x^3−0.37x^2+3.557x+51.588]dx
1/14[0.00792x^4/4−0.37x^3/3+3.557x^2/2+51.588x]20-6
51.70094
Therefore, the average newspaper circulation from 1986 to 2000 was 51.70094.
Part b:
Now, the equation is obtained as
0.00792x^3−0.37x^2+3.557x+51.588=51.70094
0.00792x^3−0.37x^2+3.557x−0.11294=0
Obtain the value of x using an online graphing calculator as follows:
Thus, the value of x becomes 13.481
Hence, 1993 is the year of the closest average circulation
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