The mass (in grams) of a radioactive sample is modeled by

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

Problem

m(t)=m_0e^{-0.00042\ln(t-1950)}

, where

t

is the calendar year. In 2023 the sample’s mass is measured to be

0.38\,\text{g}

. Find

m_0

, the mass the sample had in 1950.