1. Caffeine Problem  The half-life of caffeine is 5 hours; this means that approximately ½ of the caffeine in the bloodstream is eliminated every 5 hours.  Suppose you drink a can of Instant Energy, that contains 80 mg of caffeine.

2.  How much caffeine will remain in your bloodstream after 5 hours? 10 hours? 1 hour? 2 hours? hour0123456 Caffeine (mg) 8040

3.  Write an exponential function to model the amount of caffeine remaining in the blood stream t hours after the peak level.  Use exponential regression

4. Bacteria Growth  The bacteria count in a heated swimming pool is 1500 bacteria per cubic centimeter on Monday morning at 8 AM, and the count doubles each day thereafter.  What bacteria count can you expect on Wednesday at 8 AM?

5. DaysBacteria 01500 13000 26000 312 000 4 5 6

6.  Suppose we want to know the expected bacteria count at 2 PM Thursday, 3.25 days after the initial count. Use the values in your table to estimate the number of bacteria.

7.  At what time will the bacteria count be 25670280?

8. Intro to inverses  How to undo exponential fumctions

9. Logarithms  The inverse of an exponential is a logarithm  y = b x  therefore  log b y = x

10. Practice Problems  Log 10 1=?  Aka 10 to the power of what =1  Log 6 36 =  Log 4 x= 3