A model rocket is lauriched with an initial upward velocity of \( 204 ft / s \) .
\( h = 204 t - 16 t ^ { 2 } \)
Find all values of \( t \) for which the rocket's height is \( 100 \) feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
t = 0.5 or t = 12
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.
