A radioactive sample has mass after years

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A radioactive sample has mass

18\text{ mg}

after

10

years. Its rate of change satisfies

\dfrac{dy}{dt}=-0.07y

, where

t

is in years. Which of the following statements about the initial mass

y_0

t=0

is most accurate? (a)

y_0<18\text{ mg}

because the decay constant is positive. (b)

y_0=18\text{ mg}

because the mass is independent of time during exponential decay. (c)

y_0>18\text{ mg}

because the decay constant is negative and time is positive. (d)

y_0<18\text{ mg}

because an exponent with a negative coefficient causes the quantity to increase over time.