Question

Initially 700 milligrams of a radioactive substance was present. After 2 hours the mass had decreased by 5%. Construct an exponential model
A(t) = A0ekt
for the amount remaining of the decaying substance after t hours. Find the amount remaining after 24 hours. (Round your answer to one decimal place.)

Answer 1

amount = 700 e^(kt)
when t = 2, amount = .95(700) = 665
665 = 700 e^(2k)
.95 = e^(2k)
take ln of both sides and use log rules:
lon .95 = 2k ln e
ln .95 = 2k
k = ln.95/2

amount = 700e^(ln.95/2 t) = 700 e^(-.025647t)
plug in t = 24 and find amount

let me know what you got, I wrote my answer down

Answer 2

A(2) = A0 e^(2k) = 0.95 A0
A(24) = A0 e^(24k) = A0 (e^2k)^12 = 0.95^12 A0
700*0.95^12 = _____

This doesn't give you the value of k, but it does give the same answer for A(24)