By getting the exponential decay that models the situation, we will see that after 8 weeks she uses 0.12 cups.
We know that the first week, she uses 2 cups of sugar, and each week she uses removes one-third of what she used the previous week.
Then the second week she uses:
S₂ = 2 cups - (1/3)*(2 cups) = 2 cups*(1 - 1/3) = 2 cups*(2/3)
The third week she uses:
S₃ = 2 cups*(2/3) - (1/3)*2 cups*(2/3) = 2 cups*(2/3)^2
You already can see the pattern, at week x, she will use:
Sₓ = (2 cups)*(2/3)^(x - 1)
This is an exponential decay.
To get how much sugar does she uses after 8 weeks, we just replace x by 8 in the above equation:
S₈ = (2 units)*(2/3)^(8 - 1) = 0.12 cups of sugar.
If you want to learn more about exponentials, you can read:
https://brainly.com/question/11464095
