whats the exponential decay equation for 100 atoms that decay 1/20 per day

Answer 1

1/20 = .05

dn/dt = -.05 n

dn/n = -.05 dt

ln n = -.05 t + c

n = C e^-.05 t

n = 100 e^-.05 t

Answer 2

Hmm. Since the amount present on day n is 0.95 times the amount on day (n-1) I think the equation should be

n = 100*0.95^t
= 100 * e^{ln.95 t}

ln.95 = -.05129

I keep thinking this is absorbed into the c of the integral, but that must certainly be 100.

How to reconcile?