I believe the equation you should be using is:

A = I*e^(rt)

Where e is the natural number: e = 2.71828182846...

For the first problem, we know that A = 2I when t = 15:

2I = I*e^(15r)

2 = e^(15r)

ln2 = lne^(15r)

ln2 = 15r

r = ln2/15 = 0.0462

For the second problem, we know that I = 400, A = 120 when t = 320:

120 = 400*e^(320r)

1/3 = e^(320r)

ln(1/3) = 320r

r = ln(1/3)/320

Now, we want A = 1/2(I) = 1/2(400) = 200:

200 = 400*e^(t*ln(1/3)/320)

1/2 = e^(t*ln(1/3)/320)

ln(1/2) = t*ln(1/3)/320

t = 320*ln(1/2)/ln(1/3) = 201.8975