Question 1186442
**(a) Finding the linear function:**

Since the number of households is declining at a constant rate, we can model this situation with a linear function of the form:

f(t) = mt + b

where:

* f(t) is the projected number of households (in millions) in year t
* m is the slope (rate of change)
* b is the y-intercept (initial number of households)

We are given:

* b = 42.5 million (initial number of households at t = 0)
* m = -3.9 million households per year (decline rate, so it's negative)

Therefore, the linear function is:

f(t) = -3.9t + 42.5

**(b) Projecting households at the beginning of 2011:**

Since t = 0 corresponds to the beginning of 2004, the beginning of 2011 corresponds to t = 2011 - 2004 = 7.

We can now plug t = 7 into our linear function:

f(7) = -3.9 * 7 + 42.5
f(7) = -27.3 + 42.5
f(7) = 15.2

So, the projected number of U.S. dial-up Internet households at the beginning of 2011 is 15.2 million.