Assuming the initial rat population was 67 million, simply plug in 11 for t, so:
20051994 = 11; Eleven years have passed.
0.035 * t = 0.035 * 11 = 0.385;
n(11) = 67 * e^{(0.035*11)}
n(11) = 67 * e^{0.385 }= 67 * 1.46961 = 98.4641 (million)
1.) In windows calculator, use View>Scientific view
2.) For e^{x }use [Inv]. This changes the [ln] button to [e^{x}].
3.) Multiply by 67.
.385 [Inv][e^{x}] or [Inv][ln] or [Inv][log] on your calculator, then times 67.
e = 2.7182... > 1. So with a positive exponent, the result will also be >1. The more years pass, the greater the exponent,and the greater the result (and number of rats) will be. When you multiply by a number greater than one, the result will always be a bigger number.
11/26/2013

Michael K.