A cannonball is fired directly upward with an initial velocity of \( 600 \) feet per second. Its height above the ground at time \( t \) can be modeled with the equation
\( h = - 16 t ^ { 2 } + 600 t\)
How high does the cannonball travel before it begins to fall back to the ground? Round your answer to two decimal places if needed.
\(h_{\max}= \frac{- 600^{2}}{4(- 16)}= 5625\)
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.
