A golf ball is hit from ground level. Its path is modelled by the relation \( h = - 4.9 t ^ { 2 } + 30.6 t \) , where \( h \) is the ball's height above the ground, in metres, and \( t \) is the time, in seconds.
a) For how long will the ball travel before it hits the ground? \( A / 3 C / 1 \)
b) How long will it take for the ball to reach the maximum height? \( A / 1 C / 1 \)
c) What is the maximum height of the ball? \( A / 2 C / 1\)
a ) time = 6.245 second
b ) time = 3.2 second
c) maximum height = 47.74 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.
