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) \\ \\ (1)/(2)=e^(-0.1386t) \\ \\ ln((1)/(2))=ln(e^(-0.1386t)) \\ \\ -0.693=-0.1386t \\ \\ t=3.775`

Likewise for Amount B:


`4=10e^(-0.2t) \\ \\ (2)/(5)= e^(-0.2t) \\ \\ ln((2)/(5))=ln(e^(-0.2t)) \\ \\ -0.916=-0.2t \\ \\ t=4.58`

Similarly for Amount C:


`4=9e^(-0.3t) \\ \\ ln( (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.