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

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

$\frac{dy}{dx} =ky\\\frac{dy}{y} =kdx$

Integrate both sides

$ln y =-kx+C$

Rise to power e

$y=Ae^{-kx}$

where A=e^C

Hence this is exponential decay

Answer 2

The answer would be B