2. What is the solution to the system of equations below? Show all work and explanations that lead to your solution.
\(\left\{ \begin{array} { l } { y = 2 x - 12 } \\ { - 4 x + 2 y = 12 } \end{array} \right.\)
a. \( ( 2 , - 8 ) \)
b. \( ( 1,10 ) \)
c. Infinitely many solutions
d. No solution
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.
