Question

According to the Pew Research Center Journalism and Media, the estimated circulation of weekday newspapers, in millions, in the United States can be approximated by the formula c = -0.0166x^2 + 1.2109x + 41.708 where x is the number of years after 1940. According to the formula, in what year would the circulation of weekday newspapers be 0 million? Round to the nearest year.

Answer 1

Step-by-step explanation:

so, simply, when is c = 0 ?

0 = -0.0166x² + 1.2109x + 41.708

the solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = -0.0166

b = 1.2109

c = 41.708

x = (-1.2109 ± sqrt(1.2109² - 4×-0.0166×41.708))/(2×-0.0166) =

= (-1.2109 ± sqrt(1.46627881 + 2.7694112))/-0.0332 =

= (-1.2109 ± sqrt(4.23569001)/-0.0332 =

= (-1.2109 ± 2.058079204...)/-0.0332

x1 = (-1.2109 + 2.058079204...)/-0.0332 =

= -25.5174459... years

x2 = (-1.2109 - 2.058079204...)/-0.0332 =

= 98.46322904... years

x1 represents then a calculation backwards of 1940 - 25.5 years (≈ 1914) as the estimated starting point with 0 million sold papers.

x2 is the projected year in the future with 0 million dogs papers :

1940 + 98.46322904... = 2038.463229... ≈ 2038

based on this equation it is expected that during 2038 the circulation of weekday newspapers will drop to 0 millions.