5. The table below shows the amount of money that Philip needs to purchase a new video game system at different points in time.
Which function models the amount of money that Philip still needs at week \( x \) ?
A \( f ( x ) = 160 ( 0.8 ) ^ { x } \)
B. \( f ( x ) = 200 ( 0.8 ) ^ { x } \)
C. \( f ( x ) = 160 - 32 x \)
D. \( f ( x ) = 192 - 32 x\)
Option "B" is correct
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.
