2) Find the domain and range of the rational function \( w ( x ) = \frac { 3 x - 21 } { 3 x ^ { 2 } - 20 x - 7 } \)
A) Factor the numerator and denominator. B) Determine the point of discontinuity if it exists. C) Determine the vertical asymptote. D) Determine the horizontal asymptote. E) Graph the function. 1) Fill in the table of values to find three or four points to plot for each curve. Use a graphing calculator.
Domain \(\{ x \in R : x \neq - \frac { 1 } { 3 }\)and \(x \neq 7 \}\)
Range \(\{ w \in R : w \neq 0\) and \(w \neq \frac { 3 } { 22 } \}\)
C) \(x= -\frac{1}{3}\)
D) y=0
E) x -6 -2 -1 0 1 3 w(x) \(- \frac{3}{17}\) -\(\frac{3}{5}\) -\(\frac{3}{2}\) 3 \(\frac{3}{4}\) \(\frac{3}{10}\)
Find the solution of the exponential equation \( 16 e ^ { x } = 12 \) in terms of logarithms, or correct to four decimal places. \( x = \)
Certain radioactive material decays in such a way that the mass remaining after \( t \) years is given by the function
\( m ( t ) = 100 e ^ { - 0.01 t } \)
where \( m ( t ) \) is measured in grams. (a) Find the mass at time \( t = 0 \) . Your answer is (b) How much of the mass remains after \( 20 \) years? Your answer is Round answers to \( 1 \) decimal place.
