1. The manager of a hardware store sells batteries for \( \$ 5 \) a package. She wants to see how much money she will earn if she increases the price in \( 10 c \) increments. A model of the price change is the revenue function \( R ( x ) = - x ^ { 2 } + 10 x + 3000 \) , where \( x \) is the number of \( 10 \varphi \) increments and \( R ( x ) \) is in dollars. Explain how to determine the maximum revenue.
2. Determine the maximum revenue generated by the manager in question \( 1 \) .
\(R ( x ) = - x ^ { 2 } + 1 0 x + 3000 \)
\( - \frac { b } { 2 a } = \frac { - 10 } { 2 \times ( - 1 ) } = 5 \)
\( R ( 5 ) = - 5 ^ { 2 } + 10 \times 5 + 3000 = 3025\)
A linear function that models data is described below. Find the slope of the model. Then describe what this means in terms of the rate of change of the dependent variable per unit change in the independent variable. The linear function \( f ( x ) = - 0.41 x + 28.6 \) models the percentage of adults in a country who smoked cigarettes, \( f ( x ) \) , \( x \) years after \( 1997 \) .
The slope is \( \square \) . (Type an integer or a decimal.)
Use the quadratic formula or completing the square to determine the greater solution to
\( x ^ { 2 } + 4 x + 2 = 0 \) . Round your answer to the nearest hundredth. Record your answer and fill in the bubbles on your answer document.
