Solve the problem

Question

The function A=A₀e^-0.01386x 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 74 pounds to remain? 

 

 

 

 

 

 

( answer is 180 years but i need help step by step on how they got this answer) 

Answer 1

A=A₀e^-0.01386x

 

Where:

• A = the amount pf radioactive material left after x years = 74 pounds
• A₀ = the initial amount of radioactive material = 900 pounds
• t = years in the vault

 

A=A₀e^-0.01386x

74 = 900e^-0.01386t                    {Plugged in 74 lbs for A and 900 lbs for A₀}

74/900 = e^-0.01386t                   {Divided both sides by 900}

0.0822 = e^-0.01386t

ln(0.0822) = -0.01386t                {Take the natural log (ln) of both sides}

ln(0.0822)/(-0.01386) = t

 

Use your calculator to compute the value of t.