Solving for k in the Exponential Decay Equation: Civil Engineering Homework Help

[kriss_boy]

Homework Statement

Its back to college for me and studying for Civil Engineering Qualification. I am stuck on this one and don't really have anyone to turn to!

Homework Equations

P₁ = P₀e^-kt

The Attempt at a Solution

I need to change the subject to (k) but our lecturer did not cover this type of question!

 

[HallsofIvy]

If you are going back to college I'm sure you learned long ago that you solve an equation by "undoing" what has been done.
There have been three things done to k (and you want to solve for k):
(1) it has been multiplied by -t
(2) the exponential has been taken
(3) that has been multiplied by P₀

To undo that, do the opposite in the opposite order.
(3) To undo "multiply by P₀", do the opposite: divide by P₀. Dividing both sides of the equation by P₀ gives You P/P₀= e^-kt.
(2) To undo the exponential use its inverse function, natural logarithm.
Taking the natural logarithm of both sides give ln(P/P₀)= ln(e^-kt)= -kt.
(3) To undo the multiplication by -t, divide by -t:
I let you both sides by -t.

 

[kriss_boy]

So is the answer...

k = ln(p₁/P_o) /-t

 

[sara_87]

Yep that's right!