A bouncing toy reaches a height of \( 64 \) inches at its first peak, \( 48 \) inches at its second peak, and \( 36 \) inches at its third peak. Which explicit function represents the geometric sequence of the heights of the toy?
\( f ( x ) = 48 ( \frac { 5 } { 6 } ) ^ { x - 1 } \)
\( f ( x ) = 48 ( \frac { 3 } { 4 } ) ^ { x - 1 } \)
\( f ( x ) = 64 ( \frac { 3 } { 4 } ) ^ { x - 1 } \)
\( f ( x ) = 64 ( \frac { 5 } { 6 } ) ^ { x - 1 }\)
f(x) = 64\((\frac{3}{4})^{x- 1}\)
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.
