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The Exponential Function Quiz

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This quiz tests the work covered in Lecture 2 and corresponds to Section 1.2 of the text Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).
There is no web quiz from Wiley for this section.
There are two sections of economics quiz site that would be useful, Exponential Graphs and Exponential Functions.
The Mathematics Learning Centre has a booklet on Introduction to Exponents and Logarithms and tutors who can help you with the concepts.

There are some animations available at http://archives.math.utk.edu/visual.calculus/0/exp˙log.5/. The Java applet doesn’t require any plugins and is very useful.


 

Question 1

 
 
Which table of values correspond to exponential functions?
There may be more than one correct answer.
a)

t  0  1  2  3 4 5
P  5  6  9 142130
b)
t 0 2 4 6 8 10
P 30014772.0335.294717.29448.4726
c)
t 0 1 2 5 7 10
P 25012567.538.7519.8759.9675
d)
t  0 1 2  3  4  5 
P 1210  8  6  4  2
e)
t  0 1  2  3  4  5
P 202428.834.5641.47249.7664

 

There is at least one mistake.
For example, choice (a) should be false.
Try again, the t values are evenly spaces but the ratios are not fixed.
There is at least one mistake.
For example, choice (b) should be true.
Note that the t values are equally spaced and the ratios 300 -147- 17.2944 147 = 72.03 = ...= 8.4726 ≈ 2.04 are fixed so the function is exponential.
There is at least one mistake.
For example, choice (c) should be false.
Try again, although the ratios are fixed the t values are not evenly spaced.
There is at least one mistake.
For example, choice (d) should be false.
Try again, the t values are evenly spaces but the ratios are not fixed.
There is at least one mistake.
For example, choice (e) should be true.
Note that the t values are equally spaced and the ratios 20 24 41.472 24 = 28.8 = ...= 49.7664-≈ 8.333 are fixed so the function is exponential.
Your answers are correct
  1. False. Try again, the t values are evenly spaces but the ratios are not fixed.
  2. True. Note that the t values are equally spaced and the ratios 300 -147- 17.2944 147 = 72.03 = ...= 8.4726 ≈ 2.04 are fixed so the function is exponential.
  3. False. Try again, although the ratios are fixed the t values are not evenly spaced.
  4. False. Try again, the t values are evenly spaces but the ratios are not fixed.
  5. True. Note that the t values are equally spaced and the ratios 20 24 41.472 24 = 28.8 = ...= 49.7664-≈ 8.333 are fixed so the function is exponential.
 

Question 2

 
 
Which of the following curves are concave up?
More than one answer may be correct.
a) PIC   b) PIC
c) PIC   d) PIC

 

There is at least one mistake.
For example, choice (a) should be true.
This curve is x y = e and it is concave up.
There is at least one mistake.
For example, choice (b) should be false.
Try again, this curve is concave down.
There is at least one mistake.
For example, choice (c) should be true.
This curve is a quadratic and is concave up.
There is at least one mistake.
For example, choice (d) should be true.
This curve is y = e-x and is concave up.
Your answers are correct
  1. True. This curve is x y = e and it is concave up.
  2. False. Try again, this curve is concave down.
  3. True. This curve is a quadratic and is concave up.
  4. True. This curve is y = e-x and is concave up.
 

Question 3

 
 
Consider the exponential function below and determine which one of the following statements is true.
P(t) = 800(0.7)t
a) P describes exponential growth where the initial quantity is 800 .
b) P describes exponential decay where the initial quantity is 800.
c) P describes exponential growth where the initial quantity is 0.7.
d) P describes exponential decay where the initial quantity is 0.7 .

 

Not correct. Choice (a) is false.
Try again, the factor by which P changes is 0.7 .
Your answer is correct.
Not correct. Choice (c) is false.
Try again, read the definition of The General Exponential Function on page 11.
Not correct. Choice (d) is false.
Try again, read the definition of The General Exponential Function on page 11.
 

Question 4

 
 
The half-life of radium-226 is 1620 years. There is 100g of radium-226 in a particular sample now.
Which of the following gives the correct amount of radium-266 in 3240 years?
a) 400g.   b) 50g.
c) 25g.   d) 0g

 

Not correct. Choice (a) is false.
Try again, you have doubled the quantity twice.
Not correct. Choice (b) is false.
Try again, this is how much you would have after 1620 years.
Your answer is correct.
After 1620 years there would be 50g left and after a further 1620 years
there would be half of that left, that is 25g left.
Not correct. Choice (d) is false.
Try again, even though the sample loses 50g in the first 1620 years,
it does not lose a further 50g in the next 1620 years.