A baseball team plays in a stadium that holds \( 48000 \) spectators. With the ticket price at \( \$ 11 \) the average attendance has been \( 19000 \) . When the price dropped to \( \$ 8 \) , the average attendance rose \( 24000 \) . Assume that attendance is linearly related to ticket price.
What ticket price would maximize revenue? \( \$\) ____
1.12
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.
