Question

For the period 1990-2002, the number S (in thousands) of cellular telephone subscribers in the United States can be modeled by S=858t²+1412t+4982 where t is the number of years since 1990. In what year did the number of subscribers reach 50 million?

A 1991
B 1992
C 1996
D 2000

Answer 1

To find the year when the number of subscribers reached 50 million, we need to solve the equation S = 50,000. The correct answer is 1995.

Step-by-step explanation:

To find the year when the number of subscribers reached 50 million, we need to solve the equation S = 50,000. We can substitute this value into the equation and solve for t.

50,000 = 858t² + 1412t + 4982

Arranging this equation in standard quadratic form, we get:

858t² + 1412t - 44,018 = 0

Using the quadratic formula or factoring, we find two values for t: t ≈ -0.893 and t ≈ 5.282.

Since t represents the number of years since 1990, we add t to 1990 to find the year. Therefore, t ≈ 5.282 corresponds to the year 1990 + 5.282 ≈ 1995 in which the number of subscribers reached 50 million.

The correct answer is 1995.