If 900 pounds of materials are placed in the vault, how much time would need to pass for only 357 pounds to remain?

Question

The function A = A0e-0.01155x models the amount in pounds of a particular radioactive material stored in a concrete vault, where A0 is the original amount of material and x is the number of years since the material was put in the vault. If 900 pounds of material are placed in the vault, how much time will need to pass for only 357 pounds to remain?

***** 0 should be lower than the A like a subscript

Answer 1

Hi Brittany

 

A = A₀e^-0.01155x

We begin with 900 pound and want to know the time that will pass for only 357 pound to remain

 

357 = 900e^-0.01155x

 

We need to isolate the x (time)

 

Divide by 900

.39666... = e^-0.01155x

 

Take the natural log of both sides

 

ln (0.39666...) = -0.01155x

-0.92466 = -0.01155x

 

And finally divide by -0.01155 to solve for x

 

x = 80 years