1) The formula for the speed of a falling object is \(v = \sqrt { 64 d }\)
where \(v\) is the speed of the object in feet per second and \(d\) is the distance the object has fallen, in feet. What distance has an object fallen if its speed is \(16\) feet per second?
\(16= \sqrt{64d}\)
\(16^{2} = 256= 64d\)
\(d= \frac{256}{64} = 4\)
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.
