A local theater sold \( 110 \) tickets to a matinee play with a total revenue of \( \$ 1,334.00 \)
where they charged \( \$ 17.00 \) for an adult ticket and \( \$ 9.00 \) for a child's ticket. Using the variables \( a \) and \( c \) to represent the number of adult tickets sold and the number of children's tickets sold respectively, determine a system of equations that describes the situation.
a=43
c=67
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.
