1. Consider the function ()=3 +72 36. a. [1 pts] Find (2). b. [4 pts] Factor (). Show all your work. (Hint: You can use the fact that if ()=0, then the () must have () as a factor.) 2. Miguel decided to invest some of his money in an account gaining 3% interest compounded semiannually. He ultimately would like to purchase a $60,000 car. a. [5 pts] How much would he have to invest initially to have the necessary money in 4 years? Round your answer to the nearest whole dollar. b. [5 pts] Miguel realized he only has $20,000 to invest. If he invests all $20,000 in the same account described above, how long would it take for him to reach the $60,000 he needs? Round to the nearest whole year.

3. Note that after 5715 years a given amount of carbon-14 will have decayed to half the original amount. a. [5 pts] Find the exponential decay model for carbon-14. Round the decay constant to 6 decimal places. b. [5 pts] In 1947, earthenware jars containing what are known as the Dead Sea Scrolls were found by an Arab Bedouin herdsman. Analysis indicated that the scroll wrappings contained 76% of their original carbon-14. Estimate the age of the Dead Sea Scrolls. Round the answer to a whole number.