The table shows the numbers of us cellular subscriberships

Question

U.S. cellular subscriberships

The table shows the numbers of U.S. cellular subscriberships (in millions) from 1995 to 2008.

Assume that the number of U.S. cellular subscriberships, in millions, can be modeled by the function S(t) = 0.105t^2.531 where t is the number of years past 1985.

(a) Find the function that models the instantaneous rate of change of the U.S. cellular subscriberships.

(b) Use the second derivative to determine how fast the rate found in part (a) was changing in 1995 and 2008.

(c) Write sentences that explain the meanings of S'(28) and S"(28).