Answer:
A = Pert is formula for continuously compounded interest
A = final amount = 2000
P = principal = 1000
e = euler's number (on calculator)
r = interest rate as decimal = .075
t = time in years
Your mistake is that 7.5% as a decimal is 7.5/100 = .075
not 7.5
2000 = 1000e.075t
e.075t = 2000/1000
e.075t = 2
take natural log of both sides
ln e.075t = ln 2
.075t = ln 2
t = ln2/.075
t = 9.24 years