SOLUTION: Can you please help me with this? The amount of radioactive material, in grams, present after t days is modeled by: A(t)=600e^-0.5t a) Find the amount present after 12 days

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can you please help me with this? The amount of radioactive material, in grams, present after t days is modeled by: A(t)=600e^-0.5t a) Find the amount present after 12 days      Log On


   

Question 924217: Can you please help me with this?
The amount of radioactive material, in grams, present after t days is modeled by:
A(t)=600e^-0.5t
a) Find the amount present after 12 days.
I think I got this one.
A(12)=600e^-0.5*12
A(12)=1.487g
b)find the half-life of the material
This one I had more trouble with. I got a negative answer when I tried it.
300=600e^-0.5t
.5=e^-0.5t
log base e (.5)=-0.5t
t=(log base e (.5))/-0.5
t=-.434yrs
but that doesn't feel right...
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a) Find the amount present after 12 days.
I think I got this one.
A%2812%29=600e%5E%28-0.5%2A12%29
A%2812%29=1.487g----you got this one
b)find the half-life of the material

300=600e%5E%28-0.5t%29
300%2F600=e%5E%28-0.5t%29
.5=e%5E%28-0.5t%29
ln%28.5%29=ln%28e%5E%28-0.5t%29%29
ln%28.5%29=%28-0.5t%29ln%28e%29......ln%28e%29=1
ln%28.5%29=-0.5t
-0.693147=-0.5t
-0.693147%2F-0.5=t
t=1.386294