the growth colony of bacteria is given by the differential equation dy/dt = -y which of the following could be an approperiate model for the number t

Question

the growth colony of bacteria is given by the differential equation dy/dt = -y which of the following could be an appropriate model for the number of bactera at time t

a) y=3e^t

b) y=-1/2y^2

c) y=-1

d) y=-e^t

e)y=7e^-t

Answer 1

dy/dt = -y

-dy/y = dt

-∫(dy/y) = ∫dt

-ln(y) = t+C

ln(y) = -t+C

|y| = e^-t+C

y = e^-te^C

y = Ce^-t

Therefore, option E, y=7e^-t, is the only model that fits the general solution.

Hope this helped!