2. The table below shows values for the function \( H ( t , h )\) .
(a) (2 points) Is \( H ( t , 150 ) \) an increasing or decreasing function of \( t ?\)
(b) (2 points) Is \( H ( 4 , h ) \) an increasing or decreasing function of \( h ?\)
(c) (3 points) Fill in the blanks: The maximum value shown on this table is \( H ( \square, \square ) \)= \(\square\) .
(d) (3 points) Fill in the blanks: The minimum value shown on this table is \(H ( \square, \square )\)= \(\square\) .
decreasing
increasing
2,200,210.4
5,100,52.5
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.
