In our macro-economic models, we always input a central bank interest rate. Yet, when I go to the bank to borrow money, I get a much higher interest rate. How does a higher or lower interest rate effect lending if I can't borrow at that rate anyway?

While this is not necessarily relevant for the IB exams, it is important to keep in mind that the interest rate that we use in the macro-economic models like the AD/AS model is an approximation of cost of lending and borrowing for firms. In reality interest rates follow a spread, with the safest debt (like government debt) being subject to the 'safest' central bank rates. You as a borrower however are not a safe bet for a bank, so they will ask for an additional premium. When central banks set different interest rates, what they are adjusting is therefore essentially the lowest possible interest rate you can attain in an economy when lending to a borrower that is considered 'safe'. Any other borrower, be it bank or company, will have to pay above that rate to compensate for the default risk associated with lending to non-government institutions.
As an example, lets say you read in the newspaper that the central bank increases interest rates from 3% to 5% and you wish to borrow £100 pounds from the bank. It is not the case that you used to get 3% interest and now 5% interest as a result of the central bank policy. Rather, you used to pay an 8% interest (because you have no job and so have a high default risk) and after the central bank raised its base interest rates, your new interest is 10% - 2% higher than what you used to pay. As you see, the cost of borrowing went up by 2%, while my spread remained exactly the same: (8%-3% = 5% and 10%-5% = 5%). This is how the central bank interest rate has the ability to effect the real economy.