Question

How do you linearise the radioactive decay function properly?

So I need to put:`N(t) = N_oe^(-t/tau)` into the `y=mx+c` form with identities and I think the `-t/tau` is throwing me out here as i'm used to `lambda` with `k` as a constant.

Answer 1

The symbol `tau` is used for the mean lifetime which is equal to `1/lambda`, so `e^(-t/tau)=e^(-t/(1/lambda))=e^(-lambdat)`

`N=N_0e^-(t/tau)`

`ln(N)=ln(N_0e^-(t/tau))=ln(N_0)+ln(e^-(t/tau))`
`color(white)(ln(N))=ln(N_0)-t/tau`

Since `N_0` is a y-intercept, `ln(N_0)` will give a y-intercept.and since `-1/tau` is a constant, and `t` is a variable.

`ln(N)=y`
`ln(N_0)=c`
`t=x`
`-1/tau=m`

`y=mx+c`
`ln(N)=-t/tau+ln(N_0)`