Question

Earning interest- You deposit $1000 in an account that pays 6% annual interest compounded continuously. Find the balance at the end of 2 years.

Answer 1

1,000 * e^(.06 *2) = 1318.26
because
dx/dt = .06 x
dx/x = .06 dt
ln x = .06 t
x = e^.06 t + c
or
x = Xo e^.06 t
where Xo is initial amount because e^0 = 1