A furniture company produces tables and chairs. Each table requires \(1\) hour in the assembly center and \(1 \frac { 1 } { 3 }\) hours in the finishing center. Each chair requires \(1 \frac { 1 } { 2 }\) hours in the assembly center and \(1 \frac { 1 } { 2 }\)
hours in the finishing center. The assembly center is available \(12\) hours per day, and the finishing center is available \(15\) hours per day. Write and graph a system of inequalities that describes all possible production levels.
x + 3y/2 \(\le\) 12
4x/3 + 3y/2 \(\le\) 15
x is the number of tables and y is the number of chairs
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.
