A football is passed through the air until it hits the ground. The height \( h \) of the ball (in feet) at any given time \( t \) is modeled the quadratic equation \( h = - 2 t ^ { 2 } + 14 t + 18 \) . What will the height of the ball be after \( 8 \) seconds in the air?
\( 4 \) feet
\( 3 \) feet
\(2 \) feet
\( 14 \) feet
\(h(8) = 2 \space feet\)
3rd option is correct
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.
