I can help with the last one since i don't know the specifics of the loan thing. For the last one, though, N is the end amount of bacteria; [tex] N_{0} [/tex] is the initial amount of bacteria; e is Euler's number, which is a constant; and t is time in hours. So our equation would look like this: [tex]1432=100( e^{5k} )[/tex]. First divide both sides by 100 to get [tex]14.32= e^{5k} [/tex]. The only way you can get that k down out of the exponent is to take the natural log of both sides: [tex]ln(14.32)=ln( e^{5k} )[/tex]. Of course taking the natural log of the right side undoes the e, and the natural log of 14.32 can be found on your calculator, so we have now 2.6616 = 5k. Divide both sides by 5 to get that k = .53