Web resources available

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 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

a)		0   1   2   3  4  5  5   6   9  14 21 30
b)		0 2 4 6 8 10 300 147 72.03 35.2947 17.2944 8.4726
c)		0 1 2 5 7 10 250 125 67.5 38.75 19.875 9.9675
d)		0  1  2   3   4   5  12 10  8  6  4  2
e)		0  1  2  3  4  5 20 24 28.8 34.56 41.472 49.7664

 

There is at least one mistake.
For example, choice (a) should be false.

Try again, the 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 values are equally spaced and the ratios 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 values are not evenly spaced.

There is at least one mistake.
For example, choice (d) should be false.

Try again, the 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 values are equally spaced and the ratios are fixed so the function is exponential.

Your answers are correct

1. False. Try again, the values are evenly spaces but the ratios are not fixed.
2. True. Note that the values are equally spaced and the ratios are fixed so the function is exponential.
3. False. Try again, although the ratios are fixed the values are not evenly spaced.
4. False. Try again, the values are evenly spaces but the ratios are not fixed.
5. True. Note that the values are equally spaced and the ratios are fixed so the function is exponential.

Question 2

a)				b)
c)				d)

 

There is at least one mistake.
For example, choice (a) should be true.

This curve is 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 and is concave up.

Your answers are correct

1. True. This curve is 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 and is concave up.

Question 3

Consider the exponential function below and determine which one of the following statements is true.

a)		describes exponential growth where the initial quantity is
b)		describes exponential decay where the initial quantity is
c)		describes exponential growth where the initial quantity is
d)		describes exponential decay where the initial quantity is

 

Not correct. Choice (a) is false.

Try again, the factor by which changes is

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