An exponential decay model describes the activity (in becquerels) of a radioactive tracer

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

Problem

An exponential decay model

A(t)=A_0 e^{-0.018t}

describes the activity (in becquerels) of a radioactive tracer, where

t

is in days. Laboratory readings show

A(4)=2.80\text{ Bq}

and

A(12)=2.30\text{ Bq}

. Determine whether these two readings are consistent with the model to within

2\%

. Answer “Yes” if the implied values of

A_0

differ by at most

2\%

, otherwise answer “No”.