2. Construct a rational function \( f ( x ) \) such that \( f ( x ) \) satisfies following properties.
\( | f ( x ) | \) approaches infinity as \( x \) goes to \( - 3,1,4 \) .
Roots of \( f ( x ) \) are \( x = 0,5 \) .
\( f ( x ) \) approaches \( 2 \) as \( x \) goes to infinity.
\(f(x)= \frac{2x^2(x- 5)}{(x+ 3)(x- 1)(x- 4)}\)
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.
