Rodolpho uses a prepaid gas card to spend \(\$ 35\) each week for gas. After the first week, he has
\(\$ 140\) left on the card. After the second week he has \(\$ 105 ,\) and so on. Which equation represents the cash balance on his card after \(t\) weeks?
\(y = 175 + 35 t\)
\(y = - 35 t + 175\)
\(y = 245 - 35 t\)
\(y = - 35 t + 140\)
y=-35t+175
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.
