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.
At time t=0 ;mass=100 gms
At time t=20 ;mass=81.8 gms
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
