4. (5 points) In a certain kind of savings account, the amount of money in dollars after 12 months can be represented by the function S(r) = 2000er, where r is the interest rate. If the interest rate is 6 percent the amount in the account after 12 months is is 2,123.67 dol- lars. If the interest rate is 9 percent, the amount in the account after 12 months is 2188.34 dollars. What property of this function, and what theorem, guarantees that there is an interest rate between 6 percent and 9 percent that will yield exactly 2, 150 dollars in the account after 12 months? 5. (5 points) Evaluate the following limit. 100 lim 100 lim