The dollar value \( v(t) \) of a certain car model that is \( t \) years old is given by the following exponential function. \[ v(t)=32,000(0.78)^{t} \] Find the value of the car after 5 years and after 12 years. Round your answers to the nearest dollar as necessary. value after 5 years: value after 12 years:

W 17) Find the vertex for \( y=x^{2}+1 \). Use \( \left(\frac{-b}{2 a}, \frac{-\left(b^{2}-4 a c\right)}{4 a}\right) \) from the quadratic formula \( x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \). \( (0,-1) \) \( (0,0) \) \( (0,1) \) \( (1,0) \)

Find the slope of the line that passes through \( (8,8) \) and \( (3,7) \). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Follow the seven step strategy to graph the following rational function. \( f(\mathrm{x})=\frac{6 \mathrm{x}}{\mathrm{x}-3} \) Plot points between and beyond each x -intercept and vertical asymptote. Find the value of the function at the given value of x . x \( \mathrm{f}(\mathrm{x})=\frac{6 \mathrm{x}}{\mathrm{x}-3} \) (Simplify your answer. Type an integer or a simplified fraction.)

Find the slope of the line that passes through \( (1,6) \) and \( (5,7) \). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Find and interpret the slope of the line containing the given points. \[ (-8,-6) \text { and }(7,6) \]