44. MODELING WITH MATHEMATICS You design a frame to surround a rectangular photo. The width of the frame is the same on every side, as shown.
a. Write a polynomial that represents the combined area of the photo and the frame.
b. Find the combined area of the photo and the frame when the width of the frame is \( 4 \) inches.
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.
