finding the rate or time in a word problem on continuous growth or decay

Question

The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 7% per day. A sample of this radioactive substance was taken three days ago. If the sample has a mass of 2 kg today, find the initial mass of the sample.

Answer 1

A = Pe^rt where r = rate of change, t= time, P = original amount, A= amount after time t

2 = Pe^-.07(3)

2 = Pe^-.21

2/P = e^-.21

ln(2/P) = -.21

ln2 -lnP =- .21

lnP = ln2+ .21= 0.69+.21

lnP = .903

P = e^.903

= about 2.47 kg 3 days ago