finding the rate or time in a word problem

Question

The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 7.9%

 per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).

Answer 1

.5 = e^-.079t

ln.5= -.079t

t= ln.5/.079= about 8.774 days

= about 8 days 18 hours, 34 minutes and 34.89 seconds

general formula is

A=Pe^rt

A= ending Amount= P/2

P = starting amount=2A

r = rate of change = 7.9% = .079

t = time = ln.5/.079

e = an irrational constant= about 2.718281828...

P/2=P=e^-.079t

if you use

.5 = (1-.079)^t

t is closer to 8.3 days

for a half life

but that's not continuous compounding

so you should get less than 8.774...