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Quiz 4: Review of Differentiation

Last unanswered question  Question  Next unanswered question
 

Question 1

 
 
It is suspected that the set of data
| -t-|1.0--2.0-5.0--10.0---15.0-- y 3.5 3.9 5.3 8.7 14.34
is exponential. Find the best approximation for the given data.
a) y = 3.2e0.1t   b) y = 2× 10-4e10t
c) y = 3.5t0.13   d) 7.7 y = 3.5t

 

Your answer is correct.
We do a semi-log transformation and to 2 decimal places we find
| ----t----|1.0---2.0---5.0---10.0--15.0-- Y = lny 1.25 1.36 1.67 2.16 2.66
A scatterplot shows that the relationship between t and Y is linear. You should draw the scatterplot to verify this. So letting Y = mt + b we find m = 0.09 and b = 1.15. Thus y = e1.15e0.1t = 3.2e0.1t .
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
This equation does not define an exponential relationship.
Not correct. Choice (d) is false.
This equation does not define an exponential relationship.
 

Question 2

 
 
It is suspected that the set of data
| -t-|0.25--0.5---0.75---1.0--1.25--1.5- y 0.66 1.09 1.79 2.96 4.87 8.03
is exponential. Find the best approximation for the given data.
a) y = 0.6e0.5t   b) y = 0.4e2t
c) y = 1.7t0.7   d) 1.4 y = 4.6t

 

Not correct. Choice (a) is false.
Your answer is correct.
We do a semi-log transformation and to 2 decimal places we find
| ----t---|-0.25---0.5--0.75--1.0--1.25---1.5--- Y = ln y - 0.42 0.09 0.58 1.09 1.58 2.08
With Y = mt + b we find m = 0.09 and b = -0.92. Thus y = e- 0.92e2t = 0.4e2t .
Not correct. Choice (c) is false.
This equation does not define an exponential relationship.
Not correct. Choice (d) is false.
This equation does not define an exponential relationship.
 

Question 3

 
 
It is suspected that the following set of data
| -x-|5.0---5.5---6.0---6.5--7.0-- y 1.36 1.50 1.66 1.83 2.03
is either exponential or allometric. Find the best approximation for the given data.
a) -115x y = 2 × 10 e   b) y = 0.5e0.2x
c) y = 1.1x0.16   d) y = 0.5x6.2

 

Not correct. Choice (a) is false.
Your answer is correct.
Transforming the data by a log-log transformation and a semi-log transformation we see that the semi-log transformation is closest to linear.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
 

Question 4

 
 
The pH of a solution is defined to be pH = -log10[H+], where [H+] is its hydrogen ion concentration. Hydrochloric acid has a pH of 1, while water has a pH of 7. Which of the following is correct?
a) The number of hydrogen ions in a cup of hydrochloric acid is 106 times the number in a cup of water.   b) The number of hydrogen ions in a cup of hydrochloric acid is 10-6 times the number in a cup of water.
c) The number of hydrogen ions in a cup of hydrochloric acid is 107 times the number in a cup of water.   d) The number of hydrogen ions in a cup of hydrochloric acid is 10-7 times the number in a cup of water.

 

Your answer is correct.
[H+]HCl = -1 10 whilst [H+]H2O = -17 10
Not correct. Choice (b) is false.
Incorrect answer.
Not correct. Choice (c) is false.
Incorrect answer.
Not correct. Choice (d) is false.
Incorrect answer.
 

Question 5

 
 
Uranium-238 has a half-life of 4.46 × 109 years. A radioactive rock is found to contain 16 grams of Uranium-238. After how many years does it contain just 4 grams?
a) 4.46 × 109 years   b) 2.23 × 109 years
c) 8.92 × 109 years   d) 1.784 × 1016 years

 

Not correct. Choice (a) is false.
Incorrect answer.
Not correct. Choice (b) is false.
Incorrect answer.
Your answer is correct.
It will take two half-lives for the sample to reach a quarter of its original size, since 14 = (12)2.
Not correct. Choice (d) is false.
Incorrect answer.
 

Question 6

 
 
Which of the following transformations linearises the data?
| -x-|1--2----3----4-----5--- y 1 - 5 - 15 - 29 - 47
a) X = x2,Y = y   b) X = 1 x,Y = y
c) X = √x-,Y = y   d) X = x,Y = y

 

Your answer is correct.
Not correct. Choice (b) is false.
Incorrect answer
Not correct. Choice (c) is false.
Incorrect answer
Not correct. Choice (d) is false.
Incorrect answer