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Bismuth83
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The graph should have minor markings on the axis/minor gridlines to solve this correctly, given the answer choices are pretty close.

Please suggest if there's a smart way to solve it without the markings.
Bismuth83
A Mars rover is analyzing samples from different soil layers to determine how the presence of a radioactive isotope has changed over time. The decay of the isotope follows a predictable pattern, and the data below was recorded at various time intervals after initial measurement. The half-life of the isotope is estimated to be between 15 and 25 hours.


Based on this data, answer the following questions:

After approximately every hours, the concentration appears to halve itself.

From hour 10 to hour 30, the average rate of decay in mg/g per hour is approximately .


Attachment:
chart (6).png
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ArpitaG
I have same doubt
RajLfcMo
How the second option is 1.7? can anyone please explain?
same doubt
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1. For first drop box, 18 & 19.5 are too close to call. Especially with a statement saying half life is estimated between 15 and 25 hours.
2. For drop box 2, say ~70mg/g became ~30 mg/g in 20 hrs. so avg decay should be 1.9/2. This one was also to close to call.

Bismuth83
A Mars rover is analyzing samples from different soil layers to determine how the presence of a radioactive isotope has changed over time. The decay of the isotope follows a predictable pattern, and the data below was recorded at various time intervals after initial measurement. The half-life of the isotope is estimated to be between 15 and 25 hours.


Based on this data, answer the following questions:

After approximately every hours, the concentration appears to halve itself.

From hour 10 to hour 30, the average rate of decay in mg/g per hour is approximately .


Attachment:
chart (6).png
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Please provide the solution for the second one, as I am confused between the two options, either 1.7 or 1.9.

Thank you!
Bismuth83
A Mars rover is analyzing samples from different soil layers to determine how the presence of a radioactive isotope has changed over time. The decay of the isotope follows a predictable pattern, and the data below was recorded at various time intervals after initial measurement. The half-life of the isotope is estimated to be between 15 and 25 hours.


Based on this data, answer the following questions:

After approximately every hours, the concentration appears to halve itself.

From hour 10 to hour 30, the average rate of decay in mg/g per hour is approximately .


Attachment:
chart (6).png
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=(70-35)/(30-10)
=35/20
1.75
ArpitaG
I have same doubt
RajLfcMo
How the second option is 1.7? can anyone please explain?
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I see how your math works, barring holding up a ruler to the graph how did you arrive at those values?
Samiksha25
=(70-35)/(30-10)
=35/20
1.75
ArpitaG
I have same doubt
RajLfcMo
How the second option is 1.7? can anyone please explain?
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I don't know if it's the best way, but it split in two intervals:

drops from 70 to ~48 in a 10h period (from 10 to 20h), which gives 2.2/h
drops from 48 to ~38 in a 10h period (from 20 to 30h), which gives 1/h
Averaging the two intervals:
3.2 / 2 = 1.6 (closest to 1.7)

RajLfcMo
How the second option is 1.7? can anyone please explain?
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Hey Bismuth83, Please explain the 1st answer. Seems really difficult to comprehend.
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1. We need to figure out the half-life of the isotope and the average rate of decay in the period from 10 hours to 30 hours, based on the graph.

2. Let's set our first reference point at concentration 100 (time 0), which means that the half concentration is 50. This can be found at time 19.4, so the half time is \(19.4 - 0 = 19.4\) hours. Another reference point can be taken, for example at concentration 58 (time 15), and similarly the half time is found to be slightly less than 20 hours.

3. The average rate of decay from hours 10 to 30 can be calculated by figuring out the (negative) slope of the line from both endpoints. In other words, it's equal to \(-\frac{33 - 68}{30 - 10} = 1.75 \approx 1.8\). (Another method is to break the interval up and take the average - this can give values slightly closer to 1.8).

4. Our answer will be: D1 - 19.5 and D2 - 1.8.
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Yep, I agree with you here that the options are pretty close and the graph isn't adequately detailed. I spread out the answer choices and changed the graph.
ManifestDreamMBA
The graph should have minor markings on the axis/minor gridlines to solve this correctly, given the answer choices are pretty close.

Please suggest if there's a smart way to solve it without the markings.
Bismuth83
A Mars rover is analyzing samples from different soil layers to determine how the presence of a radioactive isotope has changed over time. The decay of the isotope follows a predictable pattern, and the data below was recorded at various time intervals after initial measurement. The half-life of the isotope is estimated to be between 15 and 25 hours.


Based on this data, answer the following questions:

After approximately every hours, the concentration appears to halve itself.

From hour 10 to hour 30, the average rate of decay in mg/g per hour is approximately .


Attachment:
chart (6).png
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