A bacteria culture starts with \( 680 \) bacteria and grows at a rate proportional to its size. After \( 4 \) hours there will be \( 2720 \) bacteria. (a) Express the population \( P \) after. \( t \) hours as a function of \( t \) .
\( P ( t ) = \)
(b) What will be the population after \( 2 \) hours? (c) How long will it take for the population to reach \( 1830 \) ? Give your answer accurate to at least \( 2 \) decimal places.
1.13
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.
