if tina deposits $500 into a bank account that earns 4.5% interest compounded continuously, how long will it take for her account to have $2500 in it

Answer 1

r = 0.045
Ai = 500

dA/dt = Ar
dA/A = r dt
ln A = r t
A = Ai e^rt

2500 = 500 e^.045 t
5 = e^.045 t
ln 5 = .045 t
so
t = ln 5/.045 =1.61/.045
= 35.8 years