Radioactive Decay Graph in y=mx+c form

[Rockerjabroni]

Homework Statement

This is an equation relating radioactivity of lead in marine core sediments in comparison with the depth of the sediment.

The equation is A_L=A₀exponential - λL/s

Where A_L = activity at depth L (Bqkg^-1)
Where A₀ = activity at depth 0 cm (Bqkg^-1)
λ = decay constant 0.031 yr^-1
L= sediment depth (cm)
s= sediment accumulation rate (cmyr_-1)

I need to make this into y=mx+C form

Homework Equations

As above.

The Attempt at a Solution

Well Ln both sides gives me

Ln A_L = Ln (A₀exponential - λL/s)

Ln A_L = (Ln A₀) + (Ln*exponential - λL/s) (which cancels)

Ln A_L = (Ln A₀) - λL/s

Ln A_L = y
Ln (A₀) = c
L= x
1/s = m

Is that correct? The graph has to be Ln A_L against L but I wasn't sure about m and c. Thanks :)

 

[Dadface]

Hello Rockerjabroni your equation is correct.If you now compare this to y=mx+c you should see that the graph has a negative slope of gradient lambda/s and intercept lnAzero.