Question

A certain chemical decomposes exponentially. Assume that 200 grams becomes 50 grams in 1 hour. How much will remain after 3 hours? Show complete solution. 

Answer 1

we have

$200e^{k\times 1}=50$

$\implies$ $e^{k}={50\over 200}\implies k=ln({50\over 200})=-1.3863$

the exponential function for decomposition therefore becomes

$A(t)=e^{-1.3863t}$

grams remaining after 3 hours

when t=3

$A(3)=e^{-1.3863(3)}=3.1249 grams$