MAT 117 Unit D Problem Set
Directions: Show all work.
1. Consider the function ??(??) = ?? ! + 7?? ” ? 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.

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