A lamp with a parabolic reflector is shown in the figure. The bulb is placed at the focus, and the focal diameter is \( 12 cm \) .
(a) Find an equation of the parabola.
(b) Find the diameter \( d ( C , D ) \) of the opening, \( 20 cm \) from the vertex.
\(\text { (a) } y ^ { 2 } = 12 x \quad \text { (b) } 8 \sqrt { 15 } \approx 31 cm\)
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.
