Answer:
- 0 < y < 300·0.96^t
- 0 < y ≤ 400·0.938^t
Step-by-step explanation:
When a quantity changes exponentially by a fraction r in some time period t, the quantity is multiplied by 1+r in each period. That is the quantity (y) as a function of t can be described by ...
y = y0·(1+r)^t
where y0 is the initial quantity (at t=0).
Here, the problem statement gives us two quantities and their respective rates of change.
<u>Treatment A</u>
y0 < 300, r = -0.04, so the remaining amount is described by ...
y < 300·0.96^t
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Treatment B
y0 ≤ 400, r = -0.062, so the remaining amount is described by ...
y ≤ 400·0.938^t
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When we graph these, we realize these inequalities allow the quantity of each substance to be less than zero. Mathematically, those quantities will approach zero, but not equal zero, so we can put 0 as a lower bound on the value of y in each case:
- 0 < y < 300·0.96^t
- 0 < y ≤ 400·0.938^t
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<em>Comment on these inequalities</em>
We suspect your answer choices will not be concerned with the lower bound on y.
