Question

The amount of bacteria y in a petri dish grows according to the equation dy/dt=ky where k is a constant and t is measured in hours. If the ammount of bacteria triples in 10 hours, then k is apx....

Answer 1

the amount of bacteria triples in 10 hours\[y(10) = 3y(0)\]then we need to solve the DE\[\frac{dy}{dt} = ky\]\[\frac{dy}{y} = k dt\]integrate both sides using the limits given\[\int\limits_{y(0)}^{y(10)}\frac{dy}{y}= \int\limits_{0}^{10}kdt\]and then solve for k

Answer 2

ln y=kt+c
ln 3 =k(10hr)+0
k=(ln3)/10=0.109861 calculator