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Chapter 1: Problem 7
Find the slope of the line that passes through the given pair of points. $$ (-2,3) \text { and }(4,8) $$
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The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is \(\$ 140 ;\) the quantity demanded each month is 1000 when the unit price is \(\$ 110 .\) The suppliers will market 750 espresso makers if the unit price is \(\$ 60\) or higher. At a unit price of \(\$ 80\), they are willing to market 2250 units. Both the demand and supply equations are known to be linear. a. Find the demand equation. b. Find the supply equation. c. Find the equilibrium quantity and the equilibrium price.
Entomologists have discovered that a linear relationship exists between the rate of chirping of crickets of a certain species and the air temperature. When the temperature is \(70^{\circ} \mathrm{F}\), the crickets chirp at the rate of 120 chirps/min, and when the temperature is \(80^{\circ} \mathrm{F}\), they chirp at the rate of 160 chirps/min. a. Find an equation giving the relationship between the air temperature \(T\) and the number of chirps/min \(N\) of the crickets. b. Find \(N\) as a function of \(T\) and use this formula to determine the rate at which the crickets chirp when the temperature is \(102^{\circ} \mathrm{F}\).
Find an equation of the line that satisfies the given condition. The line passing through \((-5,-4)\) and parallel to the line passing through \((-3,2)\) and \((6,8)\)
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.
For each supply equation, where \(x\) is the quantity supplied in units of 1000 and \(p\) is the unit price in dollars, (a) sketch the supply curve and (b) determine the number of units of the commodity the supplier will make available in the market at the given unit price. $$ p=2 x+10 ; p=14 $$
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