The number of households using broadband Internet...

The number of households using broadband Internet connections, such as cable and DSL, increased from 6 million in 2001 to 24 million in 2007. (a) Find a linear function given by B(x) = m(x - x1) + y1 that models these data, where x is the year and B(x) is in millions. (b) Use B(x) to estimate the years when the number of households using broadband Internet connections was 18 million or more. Assume that the domain of B is 2001 to 2009. (a) B(x) = 3(x - 2001) + 6 (Do not simplify. Use integers or decimals for any numbers in the expression.) (b) The number of households using broadband Internet was 18 million or more from 2005 to 2009.

Transcript

00:01 So in this problem, they tell us that the number of households using broadband internet connections like cable and dsl increased from $6 million in 2001 to $24 million in the year 2007.

00:11 So in part a of this problem, what we want to do is to write a linear function in the given form, b of x is equal to m times the quantity of x minus x of 1 plus y sub 1, that models these data where x is the year and b of x is in millions.

00:30 So the key thing in this one is that x is in fact going to be the specific year.

00:34 So what we need to do first is we need to find the slope of this line.

00:38 That would be our m value.

00:39 Okay.

00:40 Remember, to find the slope, we have to find the change in our y values over the change in our x.

00:44 Well, the y values in this case would be the number of people using the surface.

00:48 So we'd have 24 million minus the 21 million.

00:52 Or excuse me, minus the 6 million.

00:54 Not really sure where 21 came from.

00:56 So 24 minus 6 over, it's going to be the change in the years.

00:59 So that would be 2007 minus 2001.

01:02 All right.

01:03 Well, let's go ahead and simplify.

01:04 Well, 24 minus 6 is equal to 18.

01:08 And in 2007 minus 2001 would equal to 6.

01:12 Well, 18 divided by 6 is equal to 3.

01:15 Perfect.

01:16 Okay.

01:17 So now what we're going to do is we're going to substitute 3 in place of that.

01:22 So we have b of x equals 3 times the quantity.

01:25 Now, in this particular case, b of x is in millions.

01:28 So we actually don't need to substitute all the zeros just like we did here.

01:33 So for our x sub 1 and y sub 1 values, we can use any ordered pair...

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