A dumpster in the shape of a rectangular prism has a volume of \( 240 \) cubic feet. The length of the dumpster is \( 4 \) feet leas than twice the width w, and the height is \( 1 \) foot less than the width.
Find the equation, in terms of w, that could be used to find the dimensions of the dumpster in feet. Your answer should bel in the form of a polynomial equals a constant.
Provide your answer below:
2w^3-6w^2+4w-240=0
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.
