The following table shows the numbers of U.S. cellular subscriberships (in millions) from 1985 to 2002.

Source: The CTIA Semi-Annual Wireless Industry Survey
Assume that the number of U.S. cellular subscriberships, in millions, can be modeled by the function , where t is the number of years past 1980. Find the function that models the instantaneous rate of change of the U.S. cellular subscriberships.

Question

The following table shows the numbers of U.S. cellular subscriberships (in millions) from 1985 to 2002. ​

Source: The CTIA Semi-Annual Wireless Industry Survey
Assume that the number of U.S. cellular subscriberships, in millions, can be modeled by the function  , where t is the number of years past 1980. Find the function that models the instantaneous rate of change of the U.S. cellular subscriberships.
​

Quizplus · Accepted Answer

The instantaneous rate of change is the derivative of the function that models the U.S. cellular subscriberships. So, we need to differentiate the given function with respect to t.

f(t) = 2.956t^2 + 33.84t + 7.848

f'(t) = 5.912t + 33.84

So, the function that models the instantaneous rate of change of the U.S. cellular subscriberships is f'(t) = 5.912t + 33.84. This matches option B.

The Following Table Shows the Numbers of U