The material put into the vault

Question

The function A= Aoe^-0.01155x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 900 pounds of the material are placed in the vault, how much time will need to pass for only 159 pounds to remain?

 

160 years

150 years

300 years

155 years

Answer 1

Set

 

159 = 900 e^-0.01155x

 

and solve for x.

 

159/900 = e^-0.01155x

 

ln(159/900) = -0.01155x

 

x = -ln(159/900) / 0.01155 = ? years