Definition 24 the absolute value of a real number x

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Unformatted text preview: re we go again... 122 Linear and Quadratic Functions 1. Since R = xp, we substitute p(x) = −1.5x + 250 from Example 2.1.6 to get R(x) = x(−1.5x + 250) = −1.5x2 + 250x 2. Using Definition 2.3, we get the average rate of change is R(50) − R(0) 8750 − 0 ∆R = = = 175. ∆x 50 − 0 50 − 0 Interpreting this slope as we have in similar situations, we conclude that for every additional PortaBoy sold during a given week, the weekly revenue increases $175. 3. The wording of this part is slightly different than that in Definition 2.3, but its meaning is to find the average rate of change of R over the interval [50, 100]. To find this rate of change, we compute ∆R R(100) − R(50) 10000 − 8750 = = = 25. ∆x 100 − 50 50 In other words, for each additional PortaBoy sold, the revenue increases by $25. Note while the revenue is still increasing by selling more game systems, we aren’t getting as much of an increase as we did in part 2 of this example. (Can you think of why this would hap...
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