Answer:
Option
c
Explanation:
Given that the quantity decreases at a rate that is proportional to the current value of the quantity.
This can be expressed as
rate of change of y = derivative of y
=y'=-ky
where k is the constant of proportionality
This differential equation is linear and can be solved by separation of variables
[tex]\frac{dy}{dx} =ky\\\frac{dy}{y} =kdx\\\\[/tex]
Integrate both sides
[tex]ln y =-kx+C[/tex]
Rise to power e
[tex]y=Ae^{-kx}[/tex]
where A=e^C
Hence this is exponential decay
