A parent peak (or molecular ion) with an odd mass to charge ratio (m/z) is likely to have 

In the carbon NMR of this combined spectra problem, there is a peak in the carbon NMR at 207. What functional group is responsible for this carbon signal?

Suppose the demand for a product x weeks after it launches is given by

**Partial Credit Problem** ( 6 points total) Note: To receive any credit, show all supporting work and use the Calculus techniques developed not the shortcuts with your calculator unless otherwise indicated.    For the function

Iodine-125 is a radioactive substance used in the treatment of some cancers. The amount of Iodine-125 in nanograms at time t days is modeled by: 

Extra Credit (earn up to 3 points) Can you have a point on the graph of a function that is both an inflection point and a critical point?  Explain your answer and provide a sketch to receive any credit.  

Solve  for t.  Round answer to two decimal places. 

**Partial Credit Problem**  (8 points total) Note: To receive any credit, show all supporting work and use the Calculus techniques developed not the shortcuts with your calculator unless otherwise indicated.  You may use either the first or second derivative test and show all work to receive credit.  The annual profit function for a manufacturer of precision gauges is modeled by the function

For the graph given below match the point indicated with the most appropriate description. 

**Partial Credit Problem**  (3 points total) Indicate if the following statement is true or false. To earn full credit,  If the statement is false, explain why or give an example that disproves the statement in your submitted handwritten work.   True or False: For a function the average rate of change is the same as the instantaneous rate of change.