A car rental company offers two plans for renting a car. You calculate how many miles you need to drive for the unlimited miles plan to make more financial sense.
Plan A: \( 30 \) dollars per day and \( 17 \) cents per mile.
Plan B: \( 50 \) dollars per day with free unlimited mileage.
The miles you drive must be greater than or equal to \(\square\) miles in order for Plan B to save you money. Be sure to round the mileage to the nearest whole mile.
2
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.
