
Linearizing
Im in need of some serious help.
I'm given the problem of the theoretical radioactive decay.
N=(N0)(e^(.693t/t½))
It needs to look like y=mx+b
t½= t sub 1/2
N0= N sub zero
y=N/No
This is linearizing equations and I dont even know where to begin. Any help at all?

Hi Chayned,
Let's define $\displaystyle \lambda = t_{\frac{1}{2}}$ . We have
$\displaystyle N=N_0\cdot e^{\left(\dfrac{0.693t}{\lambda}\right)}$
Well a good start would be to log both sides with base e (You will see why in a minute)
$\displaystyle \implies \ln(N)=\ln \left\{N_0\cdot e^{\left(\dfrac{0.693t}{\lambda}\right)}\right\}$
$\displaystyle \implies \ln(N)=\ln(N_0)+\ln \left\{e^{\left(\dfrac{0.693t}{\lambda}\right)}\right\}$ Since $\displaystyle \ln (ab) \equiv \ln (a) + \ln (b)$
$\displaystyle \implies \ln (N)=\frac{0.693t}{\lambda}+ \ln (N_0)$ Since $\displaystyle \ln (e^a) \equiv a$
$\displaystyle \implies \ln (N)=\frac{0.693}{\lambda} \cdot t + \ln (N_0)$ Which is of the form $\displaystyle y=mx+b$ where $\displaystyle y=\ln (N)~,~m=\frac{0.693}{\lambda}~,~x=t$ and $\displaystyle b=\ln (N_0)$