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Chapter 1: Problem 23
Evaluate (if possible) the function at each specified value of the independent variable and simplify. \(g(t)=4 t^{2}-3 t+5\) (a) \(g(2)\) (b) \(g(t-2)\) (c) \(g(t)-g(2)\)
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Find the difference quotient and simplify your Answer: $$f(x)=5 x-x^{2}, \quad \frac{f(5+h)-f(5)}{h}, \quad h \neq 0$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring.
The cost per unit in the production of an MP3 player is 60 dollars. The manufacturer charges 90 dollars per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by 0.15 dollars per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of 87 dollars per MP3 player for an order size of 120 ). (a) The table shows the profits \(P\) (in dollars) for various numbers of units ordered, \(x .\) Use the table to estimate the maximum profit. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Units, } x & 130 & 140 & 150 & 160 & 170 \\\\\hline \text { Profit, } P & 3315 & 3360 & 3375 & 3360 & 3315 \\\\\hline\end{array}$$ (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x ?\) (c) Given that \(P\) is a function of \(x,\) write the function and determine its domain. (Note: \(P=R-C\) where \(R\) is revenue and \(C\) is cost.)
(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(1)=4, \quad f(0)=6$$
The median sale prices \(p\) (in thousands of dollars) of an existing one-family home in the United States from 2000 through 2010 (see figure) can be approximated by the model \(p(t)=\left\\{\begin{array}{ll}0.438 t^{2}+10.81 t+145.9, & 0 \leq t \leq 6 \\ 5.575 t^{2}-110.67 t+720.8, & 7 \leq t \leq 10\end{array}\right.\) where \(t\) represents the year, with \(t=0\) corresponding to \(2000 .\) Use this model to find the median sale price of an existing one-family home in each year from 2000 through \(2010 .\) (Source: National Association of Realtors) (GRAPH CAN'T COPY)
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