A ball is thrown upward from a height of \( 640 \) feet above the ground, with an initial velocity of \( 96 \) feet per second. From physics it is known that the velocity at time t is \(v ( t ) = 96 - 32 t\) feet per second.
a) Find \( s ( t ) \) , the function giving the height of the ball at time t.
b) How long will the ball take to reach the ground?
c) How high will the ball go?
a s(t)=t(96-32t)
b
c
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.
