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Chapter 1: Problem 36
Find an equation of the line that has slope \(m\) and \(y\) -intercept \(b\). $$ m=-2 ; b=-1 $$
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The annual sales (in billions of dollars) of global positioning system (GPS) equipment from the year 2000 through 2006 follow \((x=0\) corresponds to the year 2000 ): $$ \begin{array}{lccccccc} \hline \text { Year, } \boldsymbol{x} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Annual Sales, } \boldsymbol{y} & 7.9 & 9.6 & 11.5 & 13.3 & 15.2 & 16.0 & 18.8 \\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the equation found in part (a) to estimate the annual sales of GPS equipment for 2008 , assuming that the trend continued.
Find an equation of the line that satisfies the given condition. The line passing through the point \((a, b)\) with slope equal to zero
Cost of A CommoDITY A manufacturer obtained the following data relating the cost \(y\) (in dollars) to the number of units \((x)\) of a commodity produced:$$ \begin{array}{lcccccc} \hline \text { Units } & & & & & & \\ \text { Produced, } x & 0 & 20 & 40 & 60 & 80 & 100 \\ \hline \begin{array}{l} \text { Cost in } \\ \text { Dollars, } \boldsymbol{y} \end{array} & 200 & 208 & 222 & 230 & 242 & 250 \\ \hline \end{array} $$ a. Plot the cost \((y)\) versus the quantity produced \((x)\). b. Draw a straight line through the points \((0,200)\) and \((100,250)\) c. Derive an equation of the straight line of part (b). d. Taking this equation to be an approximation of the relationship between the cost and the level of production, estimate the cost of producing 54 units of the
The point \((1, k)\) lies on the line with equation \(3 x+4 y=\) 12 if and only if \(k=\frac{9}{4}\).
The number of U.S. dialup Internet households stood at \(42.5\) million at the beginning of 2004 and was projected to decline at the rate of 3.9 million households per year for the next 6 yr. a. Find a linear function \(f\) giving the projected U.S. dial-up Internet households (in millions) in year \(t\), where \(t=0\) corresponds to the beginning of 2004 . b. What is the projected number of U.S. dial-up Internet households at the beginning of 2010 ?
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