SOLUTION: I'm really struggling with this problem: The amount of radioactive material, in grams, present after t days is modeled by A(t)=500e to the -0.05t (-0.05t is the exponent)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I'm really struggling with this problem: The amount of radioactive material, in grams, present after t days is modeled by A(t)=500e to the -0.05t (-0.05t is the exponent)       Log On


   

Question 35470: I'm really struggling with this problem:
The amount of radioactive material, in grams, present after t days is modeled by
A(t)=500e to the -0.05t (-0.05t is the exponent)
a)What is the initial amount of material?
b)How much material is left after 10 days?
c)Find the half-life of the material.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
a.)A(t)=500e^(-0.05t)
A(0)=500(1)
Initially, the amount was 500 grams.
b.)A(t)=500e^(-0.05t)
A(10)=500e^(-0.5)
Since I do not have a calculator with 'e', I'll let you solve the rest.
c.)250=500e^(-.05t) the end result is half of the initial (500) so (250)
.5 = e^(-.05t)
ln .5 = -.05t take the natural log of each side
(ln .5)/(-.05) = t
The time for half life of the radioactive element is about 13.86 days.