Andrew measures they 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 function that models this situation where Y is the amount of substance and X is time in days.
use your equation for problem 28 to complete the chart.
amount = 100 (1/2)^(t/3) , where t is in days
No idea what problem 28 is, so .....
0=100
3=50
6=25
9=12.5
12=6.25
To write an exponential function that models the situation, we need to use the formula for exponential decay.
The general formula for exponential decay is:
Y = Y₀ * (1/2)^(X / T)
Where:
- Y is the amount of substance at a given time (in this case, it starts at 100 moles and decreases over time).
- Y₀ is the initial amount of substance (100 moles in this case).
- X is the time (in days).
- T is the half-life of the substance (3 days in this case).
Substituting the given values into the equation, we get:
Y = 100 * (1/2)^(X / 3)
Now, let's complete the chart using this equation for different values of X:
| X | Y |
-----------------
| 0 | 100 |
| 3 | 50 |
| 6 | 25 |
| 9 | 12.5 |
| 12 | 6.25 |
| ... | ... |
In this chart, X represents the number of days elapsed and Y represents the remaining amount of the substance in moles. As time progresses, the substance will decrease by half every 3 days.