Question of the Day: ACT Science Biology 12 20 2020

[David Young]

A spectrophotometer measures specific light wavelengths emitted by a sample. The readings of the samples are compared to those on a standard curve of known values. The standard curve creates a line and the equation of this line can be used to extrapolate the concentration of a given substance in samples whose spectrophotometric measurements fall within range of the curve.

A scientist measures a sample and finds that it has an absorbance of 5.75. What is the concentration of substance in this sample?
11.375
11.25
11.5
Cannot be determined

https://www.varsitytutors.com/act_science-question-of-the-day

Not sure I would have used the word extrapolate or maybe even range here.

DAY

-- 
David Young
Fayetteville
Mathematics - Sciences - Tech
dayo...@gmail.com


http://militantgrammarian.com/DAY/

"Just because it did not happen does not mean it isn't True."
-Some Writer in Fayetteville

[John Hanna]

Interpolate is to estimate values between known values (did this a lot with logs before calcs!).

Extrapolate is to estimate values beyond (before/after) known values.

 

In your function, 5.75 is beyond the known range [.5…4] of the function.

 

Be Excellent,

     John2.71828Hanna

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[John Hanna]

And ‘range’ (absorbance) is appropriate.

 

 

Be Excellent,

     John2.71828Hanna

 

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of David Young
Sent: Sunday, December 20, 2020 5:32 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] Question of the Day: ACT Science Biology 12 20 2020

 

A spectrophotometer measures specific light wavelengths emitted by a sample. The readings of the samples are compared to those on a standard curve of known values. The standard curve creates a line and the equation of this line can be used to extrapolate the concentration of a given substance in samples whose spectrophotometric measurements fall within range of the curve.

--

[Landy Godbold]

But doesn't the need to extrapolate mean that the sample value does NOT "fall within the range of the curve"...?

cheers

----- Original Message -----
From: "John Hanna" <jeh...@optonline.net>
To: "tinspire" <tins...@googlegroups.com>
Sent: Sunday, December 20, 2020 7:18:18 PM
Subject: RE: [tinspire] Question of the Day: ACT Science Biology 12 20 2020

And ‘range’ (absorbance) is appropriate.





Be Excellent,

John2.71828Hanna



From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of David Young
Sent: Sunday, December 20, 2020 5:32 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] Question of the Day: ACT Science Biology 12 20 2020



A spectrophotometer measures specific light wavelengths emitted by a sample. The readings of the samples are compared to those on a standard curve of known values. The standard curve creates a line and the equation of this line can be used to extrapolate the concentration of a given substance in samples whose spectrophotometric measurements fall within range of the curve.

A scientist measures a sample and finds that it has an absorbance of 5.75. What is the concentration of substance in this sample?
11.375
11.25
11.5
Cannot be determined

https://www.varsitytutors.com/act_science-question-of-the-day

Not sure I would have used the word extrapolate or maybe even range here.

DAY



--
David Young
Fayetteville
Mathematics - Sciences - Tech

dayo...@gmail.com <mailto:dayo...@gmail.com>

http://militantgrammarian.com/DAY/

"Just because it did not happen does not mean it isn't True."
-Some Writer in Fayetteville

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[John Hanna]

AHA! So the graph is inverted: domain is the vertical axis and range is the horizontal axis. 'range' should be 'domain'.


Be Excellent,
John2.71828Hanna

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[David A. Young]

So why would you not say interpolate?

DAY

David A. Young

Mathematics, Sciences, and Technology

Fayetteville, AR

dayo...@gmail.com

On Dec 20, 2020, at 6:16 PM, John Hanna <jeh...@optonline.net> wrote:



Interpolate is to estimate values between known values (did this a lot with logs before calcs!).

Extrapolate is to estimate values beyond (before/after) known values.

 

In your function, 5.75 is beyond the known range [.5…4] of the function.

 

Be Excellent,

     John2.71828Hanna

 

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of David Young
Sent: Sunday, December 20, 2020 5:32 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] Question of the Day: ACT Science Biology 12 20 2020

 

A spectrophotometer measures specific light wavelengths emitted by a sample. The readings of the samples are compared to those on a standard curve of known values. The standard curve creates a line and the equation of this line can be used to extrapolate the concentration of a given substance in samples whose spectrophotometric measurements fall within range of the curve.

<image001.png>

To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/001c01d6d72e%2497b72d00%24c7258700%24%40optonline.net.

[David A. Young]

I’m thinking it is a bad question, filled with chances to get confused. A good mathematics student might “know too much” to see past the issues and arrive at the correct answer.

DAY

David A. Young
Mathematics, Sciences, and Technology
Fayetteville, AR
dayo...@gmail.com

> On Dec 20, 2020, at 9:16 PM, John Hanna <jeh...@optonline.net> wrote:
>
> AHA! So the graph is inverted: domain is the vertical axis and range is the horizontal axis. 'range' should be 'domain'.

> To view this discussion on the web visit https://groups.google.com/d/msgid/tinspire/002f01d6d747%2499daee00%24cd90ca00%24%40optonline.net.

[John Hanna]

Not a bad question, but have not seen the word 'extrapolate' recently on mathematics content. I would not have used 'extrapolate' or 'interpolate'.
More likely, something like:
"... can be used to [determine/estimate/predict] the concentration ..."

Even though 'extrapolate' is the still appropriate word!


Here's what I recall about linear interpolation (approximation):

log(3) = .4771
log(4) = .6021

Interpolate log(3.75)
Extrapolate log(4.2) (log(5) not given!)
With logs, all we did was 'interpolate' from the tables in the back of the book.
All deprecated thanks to technology.

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[John Hanna]

Decided that there’s something wrong about the graph: why use ‘y’ and ‘x’ when the domain is ‘Absorbance’ and the range is ‘Concentration’ per the text?

 

So was the answer 11.5 (5.75*2)?

 

 

Be Excellent,

     John2.71828Hanna

 

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of David Young
Sent: Sunday, December 20, 2020 5:32 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] Question of the Day: ACT Science Biology 12 20 2020

 

A spectrophotometer measures specific light wavelengths emitted by a sample. The readings of the samples are compared to those on a standard curve of known values. The standard curve creates a line and the equation of this line can be used to extrapolate the concentration of a given substance in samples whose spectrophotometric measurements fall within range of the curve.

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[Tom Lake]

If the scientist is measuring the absorbance, then shouldn't that be the independent variable (X-Axis) and concentration be the dependent variable (Y-Axis)? If so, then the domain would be absorbance and the range would be the concentration.

[David A. Young]

Cannot be determined

David A. Young

Mathematics, Sciences, and Technology

Fayetteville, AR

dayo...@gmail.com

On Dec 21, 2020, at 5:20 AM, John Hanna <jeh...@optonline.net> wrote:



Decided that there’s something wrong about the graph: why use ‘y’ and ‘x’ when the domain is ‘Absorbance’ and the range is ‘Concentration’ per the text?

 

So was the answer 11.5 (5.75*2)?

 

 

Be Excellent,

     John2.71828Hanna

 

From: tins...@googlegroups.com <tins...@googlegroups.com> On Behalf Of David Young
Sent: Sunday, December 20, 2020 5:32 PM
To: tinspire <tins...@googlegroups.com>
Subject: [tinspire] Question of the Day: ACT Science Biology 12 20 2020

 

A spectrophotometer measures specific light wavelengths emitted by a sample. The readings of the samples are compared to those on a standard curve of known values. The standard curve creates a line and the equation of this line can be used to extrapolate the concentration of a given substance in samples whose spectrophotometric measurements fall within range of the curve.

<image001.png>

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[Landy Godbold]

...because 5.75 does not fall within the set of tested values for Absorbance (i.e., is outside the range[sic] of the curve).

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[John Hanna]

But that is exactly what (linear) 'extrapolation' means!

This is getting odder every day.

Be Excellent,
John2.71828Hanna

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[David A. Young]

That’s why I don’t know why they did not use interpolation.
DAY

David A. Young
Mathematics, Sciences, and Technology
Fayetteville, AR
dayo...@gmail.com

> On Dec 21, 2020, at 12:21 PM, John Hanna <jeh...@optonline.net> wrote:
>
> But that is exactly what (linear) 'extrapolation' means!

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[Ron Armontrout]

It is the difference between science folks and math folks!

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[Landy Godbold]

It is odd today, but tomorrow it will be EVEN
and then odd
and then even
.
.
.

:-)

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[Karl]

I might be a bit late to add my comments to this thread from the science guy's perspective, but here it goes.

1)   The reason the 'concentration' is the domain - i.e. the independent variable on the x-axis and the 'absorbance is the range - i.e. the dependent variable on the y-axis has to do with the way the data and the graph are obtained.  The scientist will create a solution with known concentration and then measure the resulting absorbance.  The resulting data set and graph can then be used to determine the concentration of an unknown substance/solution based on its (measured) absorbance.  "Working backwards" so to speak.

2)   Not sure why the answer would have been "cannot be determined?"  Unless they base that on the fact that the range only goes up to 4.5 and you could "extrapolate" beyond the graph but not beyond the range shown on the y-axis?  Odd indeed, like today's date (to play along with Landy's joke:)  I mean, you either can "extrapolate" or you can't, especially if the line is given and it says, " the equation of this line can be used to extrapolate."

3)   When I googled the question yesterday, something interesting happened.  Not sure if they just "rotate" different versions through the tutoring program or if they changed the one in question.  Anyway, when I searched for it, the attached came up:

Now the absorbance value of 2.75 falls within the range of the given absorbance from 0.5 - 4.0.   A concentration of 5.5 was one of the answer choices and was the correct answer.

So if anything, now they should ask to interpolate, not extrapolate.  Using John's way of phrasing it, "... can be used to [determine/estimate/predict] the concentration ..." would have avoided all this confusion about the proper terminology.

So, if the "old version" of the question is gone, good.  If that version is still in circulation, it's really just a poorly phrased question.

Karlheinz

[David Young]

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