7. \( \frac { x + 3 } { x ^ { 2 } - 1 } - \frac { 2 x - 1 } { 7 x + 2 } = \frac { 3 x - 5 } { 7 x + 2 } \)
8. An inlet water pipe can fill a tank in \( 6 \) hours. An hour after this pipe has been open a second inlet pipe is opened and, together, the tank is filled in \( 3 \) more hours. How much time would it take for the second pipe to fill the tank by itself?
7.
8. 9 hours
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.
