A boat's crew rowed \( 16 \) miles downstream, with the current, in \( 2 \) hours. The return trip upstream, against the current, covered the same distance, but took \( 4 \) hours. Find the crew's rowing rate in still water and the rate of the current.
The crew's rowing rate in still water is \(\square\) mile(s) per hour.
The rate of the current is \( \square \) mile(s) per hour.
6
2
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.
