Question

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

A. positive slope
B. negative slope
C. exponential decay
D. exponential growth

Answer 1

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