Assume the number of U.S. dial-up Internet households stood at 38.5 million at the beginning of 2004 and was projected to decline at the rate of 3.5 million households per year for the next 9 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.
f(t) = ______
(b) What is the projected number of U.S. dial-up Internet households at the beginning of 2013?
______million households

clearly the slope is -3.5

Now think f=mt+b

(a) To find the linear function f, we need to determine the equation of a straight line that represents the decline of U.S. dial-up Internet households.

Given:
Initial number of U.S. dial-up Internet households at the beginning of 2004 = 38.5 million
Rate of decline = 3.5 million households per year

Let's assign t as the number of years since the beginning of 2004.

The equation of a straight line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope (m) represents the rate of decline, which is -3.5 million households per year (since it's a decline) and the y-intercept (b) represents the initial number of U.S. dial-up Internet households at the beginning of 2004, which is 38.5 million.

Therefore, the linear function f(t) can be written as:
f(t) = -3.5t + 38.5

(b) To find the projected number of U.S. dial-up Internet households at the beginning of 2013, we need to substitute t = 9 into the linear function f(t):

f(9) = -3.5(9) + 38.5
= -31.5 + 38.5
= 7 million households

Therefore, the projected number of U.S. dial-up Internet households at the beginning of 2013 is 7 million households.

To find the linear function that gives the projected U.S. dial-up Internet households in year t, we can use the information given. We know that at the beginning of 2004 (t = 0), there were 38.5 million households. Additionally, it is projected to decline at a rate of 3.5 million households per year for the next 9 years.

(a) To find the linear function f(t), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) represents the rate of change, which in this case is -3.5 million households per year. The y-intercept (b) represents the initial number of households, which is 38.5 million.

So, the linear function f(t) = -3.5t + 38.5.

(b) To find the projected number of U.S. dial-up Internet households at the beginning of 2013 (t = 9), we substitute t = 9 into the linear function:

f(9) = -3.5(9) + 38.5
= -31.5 + 38.5
= 7 million households.

Therefore, the projected number of U.S. dial-up Internet households at the beginning of 2013 is 7 million households.