22. The equation of a cosine curve that has an amplitude of \( 5 , \) period of \( 180 ^ { \circ } , \)
phase shift of \( 90 ^ { \circ } \) right and a vertical translation of \( 8 \) units up is:
a) \( y = 5 \cos 2 ( x - 90 ^ { \circ } ) + 8 \) b) \( y = 5 \cos ( x - 90 ^ { \circ } ) + 8 \)
c) \( y = 5 \cos 2 ( x + 90 ^ { \circ } ) + 8 \) d) \( y = 5 \cos ( x + 90 ^ { \circ } ) + 8\)
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.
