Question 1186442: Assume the number of U.S. dial-up Internet households stood at 42.5 million at the beginning of 2004 and was projected to decline at the rate of 3.9 million households per year for the next 7 years.
(a) Find a linear function f giving the projected U.S. dial-up Internet households (in millions) in year t, where t = 0 corresponds to the beginning of 2004.
(b) What is the projected number of U.S. dial-up Internet households at the beginning of 2011?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **(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.
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