A computer purchased for \( \$ 950 \) loses \( 20 \% \) of its value every year. The computer's value can be modeled by the function \( v ( t ) = a \cdot b ^ { t } \) , where \( v \) is the dollar value and \( t \) the number of years since purchase.
(A) Give the function that models the decrease in value of the computer: \( v ( t ) = \) \(\square\)
(B) In how many years will the computer be worth half its original value? Round answer to \( 1 \) decimal place. \(\square\) years
A) \(950(0.8)^t\)
B) 3.1
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.
