Question

The number of U.S. cell phone subscribers (in millions) t years after 1989 is approximated by

N(t) = 0.63t² + 1.02t + 2.7 (0 ≤ t ≤ 20)

1. What does your result tell you about the number of phone subscribers during the period under consideration?
2. What are the relative extremas?

Answer 1

The N(t) is an equation of a parabola. The t is time in years after 1989 and hence the time is always positive.

a) Thus the equation captures the positive side of the parabola, and hence the phone subscribers will keep on increasing after 1989.

b) The relative extrema can be obtained by obtaining the derivative of N and equating it to zero. The value of t for this case is the extrema.

This is the number of years after 1989.

To determine the nature of the extrema, we find the second derivative of N(t).

Hence this extrema is a minimum.

The value of N(t) at t = -0.8905 will be

Hence the subscribers at this time will be 2.29 million.

Thus, the relative minimum is at (1989, 2.29 million).