Chapter 9.9 MODELING with QUADRATIC FUNCTIONS PROBLEM...

Chapter 9.9 MODELING with QUADRATIC FUNCTIONS PROBLEM #3 The sales for a gaming console for various years are listed in the table below. Sales Year | (in billions of dollars) 1992 | 0.78 1994 | 0.38 1996 | 0.18 1998 | 0.44 1999 | 1.20 Let f(t) represent the sales (in billions of dollars) at t years since 1990. A reasonable model is f(t) = 0.065t^2 - 0.68t + 1.95 Use the model to predict when the sales will be $10 billion. You must show your work.

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00:01 Okay, so for this problem, we're going to have to use a quadratic formula.

00:05 Okay.

00:06 Now, it's saying that it gives you a table of years and sales in billions of dollars, and it's asking you to find out and predict the sales what they would be, or how long it'll take for them to be $10 billion in revenue.

00:21 Okay? so we have the function here, f of x equals to 0 .0 .0 .0.

00:32 65 t squared minus point 68 t plus 1 .95.

00:41 Okay.

00:41 Now in this case, t represents time, years, and f of x represents sales in billions.

00:48 Okay, so if we're looking for 10 billion, then we want to replace f of x by 10, and we have 0 .065t minus 0 .68t squared.

01:02 Plus 1 .95.

01:04 Now, we want to subtract 10 from both sides.

01:08 So we have the equation 0 equals to 0 .065t squared minus 0 .68t minus 8 .05.

01:22 Okay.

01:22 Now, this is our quadratic function.

01:27 Now, like any quadratic function, when we solve it for zero, we need our coefficients.

01:31 Okay, we need our coefficients, a, b, and c.

01:34 So, in this case, here's a quadratic formula.

01:38 Once we pull a, b, and c, we're going to plug it into this formula to find our two answers.

01:43 Okay, so here, a would be 0 .065...

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