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Problem 10

Find the vertex, the \(x\) -intercepts (if any), and sketch the parabola. \(f(x)=3 x^{2}-4 x+2\)

Expert verified

The vertex of the parabola is \(\left(\dfrac{2}{3}, \dfrac{10}{3}\right)\). There are no \(x\)-intercepts, as the discriminant is negative. The parabola opens upwards since the leading coefficient is positive. The sketch of the parabola includes the vertex and points at \((1,1)\) and \(\left(\dfrac{1}{3},1\right)\) with no intersections on the \(x\)-axis.

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Chapter 2

LINEAR DEPRECIATION Suppose an asset has an original value of \(\$ C\) and is depreciated linearly over \(N\) yr with a scrap value of \(\$ S\). Show that the asset's book value at the end of the \(t\) th year is described by the function $$ V(t)=C-\left(\frac{C-S}{N}\right) t $$ Hint: Find an equation of the straight line passing through the points $(0, C)\( and \)(N, S)$. (Why?)

Chapter 2

The worldwide flash memory chip sales (in billions of dollars) is projected to be $$ S(t)=4.3(t+2)^{0.94} \quad(0 \leq t \leq 6) $$ where \(t\) is measured in years, with \(t=0\) corresponding to 2002\. Flash chips are used in cell phones, digital cameras, and other products. a. What were the worldwide flash memory chip sales in \(2002 ?\) b. What were the sales for 2008 ?

Chapter 2

Patricia's neighbor, Juanita, also wishes to have a rectangular-shaped garden in her backyard. But Juanita wants her garden to have an area of $250 \mathrm{ft}^{2}\(. Letting \)x$ denote the width of the garden, find a function \(f\) in the variable \(x\) giving the length of the fencing required to construct the garden. What is the domain of the function? Hint: Refer to the figure for Exercise 26. The amount of fencing required is equal to the perimeter of the rectangle, which is twice the width plus twice the length of the rectangle.

Chapter 2

Find the vertex, the \(x\) -intercepts (if any), and sketch the parabola. \(f(x)=\frac{3}{4} x^{2}-\frac{1}{2} x+1\)

Chapter 2

The rise of digital music and the improvement to the DVD format are part of the reasons why the average selling price of standalone DVD recorders will drop in the coming years. The function $$ A(t)=\frac{699}{(t+1)^{0.94}} \quad(0 \leq t \leq 5) $$ gives the projected average selling price (in dollars) of standalone DVD recorders in year \(t\), where \(t=0\) corresponds to the beginning of 2002 . What was the average selling price of standalone DVD recorders at the beginning of \(2002 ?\) At the beginning of \(2007 ?\)

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