8. The distance a marathon runner covers can be modelled by the function
\( d ( t ) = 153.8 t + 86 \) where \( d \) represents the distance in metres and \( t \) represents the time in minutes. Approximately how long will it take her to run the \( 42.2 km \) race?
A. \( 4.5 h \) B. \( 5.0 h \) C. \( 5.5 h \) D. \( 6.0 h\)
A
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.
