Question

P= P(initial)(1/2)^(t/80)

I found Half-line:80

P=Pinitial(e)^(rt)


i cant seem to find what r is.
Help

Answer 1

I assume you want to find the equivalent equation with e as its base, so

you want
.5 = e^(80r)
ln .5 = 80r lne, but ln e = 1
r = ln.5/80
= -.0086643

or

P(initial)(1/2)^(t/80) = Pinitial(e)^(rt)
(1/2)^(t/80) = e^(rt)
take ln of both sides
(t/80) (ln .5) = rt
divide by t
(ln .5)/80 = r
r = -.008664...

check:
suppose we start with an initial P of 1000
when t = 80 , we should get 500

P = 1000 e^(-.008664(80))
= 1000 e^-.693147..
= 500.000009 , not bad I would say