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The amount of water left in a cup after sitting outside in the sun can be modelled by the function
A(t) = 120((1/2)^t/3 where A(t) represents the amount of water in mL and t represents the time passed in hours.
1. how much water will be there after 24 hours? Round your answer to 2 decimal places.
2. How long it takes for the amount of water to get to 15 mL?
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The given function describes a decay process with half-life decay period of 3 hours.
24 hours after beginning of the process is 8 (eight) half-life periods, so the amount of the water after 24 hours
will be = 0.46875 mL = 0.47 mL (rounded).
It is the answer to the first question.
To answer the second question, note that = 8 = , meaning 3 (three) half lives.
So, 3*3 = 9 hours are needed in this case.
Solved and carefully explained.
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This problem has one deficiency. The 24-hours period inevitably includes day and night.
It is difficult to imagine that the same exponential function describes evaporation from the cup
simultaneously at the day and at the night period.
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At this site, there are several lessons on exponential decay/growth problems
- Solving problem on Newton Law of cooling
- Population growth problems
- Radioactive decay problems
- Carbon dating problems
- Bacteria growth problems
Look into these lessons to make your horizon wider.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.