The amount of a certain radioactive isotope present at time t is given by $\mathrm { A } ( \mathrm { t } ) = 400 \mathrm { e } ^ { - 0.02664 \mathrm { t } }$ grams, where t is the time in years that the isotope decays. The initial amount present is 400 grams. How many grams remain
After 20 years? Round to the nearest hundredth.
A) 681.48 g
B) 234.78 g
C) 379.25 g
D) 397.87 g

Question

Quizplus · Accepted Answer

To find the amount remaining after 20 years, substitute t = 20 into the equation: $ A(20) = 400 \times e^{-0.02664 \times 20} $. This calculates to approximately 234.78 grams.

The Amount of a Certain Radioactive Isotope Present at Time A(t)=400e−0.02664t\mathrm { A } ( \mathrm { t } ) = 400 \mathrm { e } ^ { - 0.02664 \mathrm { t } }A(t)=400e−0.02664t

The Amount of a Certain Radioactive Isotope Present at Time $\mathrm { A } ( \mathrm { t } ) = 400 \mathrm { e } ^ { - 0.02664 \mathrm { t } }$