A person standing close to the edge on the top of a \(140\) -foot building throws a baseball vertically upward. The quadratic function given below models the ball's height above the ground, \(s ( t )\) , in feet, \(t\) seconds after it was thrown. Complete parts (a).
\(s ( t ) = - 16 t ^ { 2 } + 64 t + 140\)
a. After how many seconds does the ball reach its maximum height? What is the maximum height? The ball reaches its maximum height of \(\square\) feet after \(\square\) seconds.
\(204\ \ \ 2\)
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.
