A ball is thrown from the stadium seats onto the field. The height of the ball above the field at any time after it is released is modelled by the function \( h ( t ) = - 0.23 ( t - \) \( 3 ) ^ { 2 } + 15 \)
The height of the ball, \( h ( t ) \) , is measured in metres, and time, \( t \) , is measured in seconds.
What is the initial height of the ball?
12.93 m
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.
