How Do You Calculate Half-Life from an Exponential Decay Equation?

[fuzzybear]

Homework Statement

Given Y=Ae-t/(lambda) find the half life in terms of A and lambda

Homework Equations

Y=Ae-t/(lambda)

The Attempt at a Solution

every time t is a multiple of lambda the relationship then becomes (lambda(n)=A/e^n), i can't figure out how that will relate, i also tried setting the equation to A/2 however that just canceled out the A. Need help!
I figured it out t(1/2)=ln(2)/lambda, however i don't know how to incorporate A into this

 

[rl.bhat]

Expression of radioactive is written as
A = Ao*e^-λt...(1)
As you have mentioned
t_1/2 = ln(2)/λ.
The equation (1) can be written as
A/Ao = e^-λt. or
Ao/A = e^λt
Take logarithm of both the side and fine the expression for λ. Put it in the t_1/2 equation.

 

[fuzzybear]

rl.bhat if i put the expression into lambda in the t_1/2 equation then i lose the lambda, i need to express it in lambda and A

 

[rl.bhat]

In that case
t_1/2 = ln(A/Ao)/λ