For a quantity satisfying with

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

For a quantity satisfying

\dfrac{dy}{dt}=ky

with

y(0)=y_0

, derive an explicit formula for the time required for the quantity to decrease to one-half of its initial value. Express your result in terms of

k

and common mathematical constants.