# andrew measures 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).write an exponential funtion that models this...

andrew measures 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).

write an exponential funtion that models this situation where y is the amount of substance and x is time in days. use your equation to complete the chart. used your data from the chart to graph your euqation. calculate the expected amount of substance if andrew had taken his measurement 9 days earlier. show your calculations and consider the trend of your graph.

DAY AMOUNT

-3 (3 days prior)

0

3

6

9

12

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### 1 Answer

The half life of the substance is 3 days and the initial amount is 100 moles. The amount of substance after t days is equal to `S(t) = 100*(1/2)^(t/3)`

To determine the amount of substance at any moment of time, after it was initially measured or before it substitute the value of t in the formula.

For instance 3 day earlier, the amount of substance would have been `100(1/2)^(-3/3)` = `100(1/2)^(-1)` = 100*2 = 200 moles. After 9 days, the amount of substance is `100*(1/2)^(9/3)` = `100(1/2)^3` = 12.5 moles. The values at the other instances of time can be estimated in a similar way.

The graph of the amount of substance versus time elapsed is: