more questions about exponential function for a decay problem

Question

Andrew measure the amount of a very unstable substance to be 100 moles.  The half life of this substance is 3 days (after 3 days, half is gone).

 

This is what I have so far to solve this table.  ( y = amount of substance and x is time in days)

 

                                    Days                       Amount

 

                                  -3(3 days prior)           200

                                       0                           100

                                       3                            50

                                       6                            25

                                       9                            12.50

                                     12                              6.25

 

(This is using y = 100(.5) ^x/3

 

 

How would I graph this information from the table?

 

How do I calculate the expected amount of substance if Andrew had take his measurement 9 days earlier?  Show the calculations and consider the trend of the graph from above.

 

              Would the calculation be   y = 100(.5) ^x/9  ?

 

thanks

Answer 1

NO!  The half life is 3 days at all times.  This implies that the material diminishes by 1/2 every 3 days.  Conversely, the material DOUBLES as you go back in time in 3 day increments.

 

Therefore, the amount of material:

 

6 days ago: 400 moles

9 days ago: 800 moles

 

The formula (exponent) wont change

 

Enter 100*.5^(x/3) in google search and it will plot it for you!  You can write a program to do this or just place dots on the graph (1/2-life numbers) and fill in the graph yourself.