Question

Please help me understand this

Answer 1

We have the equations of 3 functions and we want to find which one of them will decay the fastest to 4 grams.

This can be done by setting each expression equal to 4 and find which of them gives the smallest value of t.

For Amount A:

$4 =8e^{-0.1386t} \\ \\ \frac{1}{2}=e^{-0.1386t} \\ \\ ln(\frac{1}{2})=ln(e^{-0.1386t}) \\ \\ -0.693=-0.1386t \\ \\ t=3.775$

Likewise for Amount B:

$4=10e^{-0.2t} \\ \\ \frac{2}{5}= e^{-0.2t} \\ \\ ln(\frac{2}{5})=ln(e^{-0.2t}) \\ \\ -0.916=-0.2t \\ \\ t=4.58$

Similarly for Amount C:

$4=9e^{-0.3t} \\ \\ ln( \frac{4}{9})=ln(e^{-0.3t} ) \\ \\ -0.811=-0.3t \\ \\ t=2.073$

Thus Amount C will take the minimum time to decay to 4 grams.