Determine if 0.680 is rational or irrational and give a reason for your answer.
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Answer:
This is the same as writing y = 650(0.907)^t
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Explanation:
Exponential equations can be of the form y = a*b^t
- a = initial amount
- b = growth or decay factor
In this case, we have
- a = 650 mg to start with
- b = 1 - 0.093 = 0.907 as the decay factor
If we had exponential growth, then we'd compute 1 + 0.093 instead.
Based on those values, we go from y = a*b^t to y = 650(0.907)^t which is the same as writing
Other exponential forms are possible, but I think this form is the most intuitive. The 0.907 means that 90.7% of the sample remains after each year.