SORRY THIS WAS FOR MATH which of the following terms best describes a condition in which a quantity decrease at a rate that is proportional to the current value of the quantity …

Question

asked Sep 22, 2019 218k views

1 Answer

Michaeak · Answer 1 · 2019-09-26T22:36:36+0000

Answer:

Option

c

Step-by-step 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

$(dy)/(dx) =ky\\(dy)/(y) =kdx\\\\$

Integrate both sides

ln y =-kx+C

Rise to power e

y=Ae^(-kx)

where A=e^C

Hence this is exponential decay