## MATH1111 Quizzes

The Exponential Function Quiz
Web resources available Questions

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 Learning Hub (Mathematics) 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.

Which table of values correspond to exponential functions?
There may be more than one correct answer.
 a) $\begin{array}{ccccccc}\hfill t& \hfill 0& \hfill 1& \hfill 2& \hfill 3& \hfill 4& \hfill 5\\ \hfill P& \hfill 5& \hfill 6& \hfill 9& \hfill 14& \hfill 21& \hfill 30\end{array}$ b) $\begin{array}{ccccccc}\hfill t& \hfill 0& \hfill 2& \hfill 4& \hfill 6& \hfill 8& \hfill 10\\ \hfill P& \hfill 300& \hfill 147& \hfill 72.03& \hfill 35.2947& \hfill 17.2944& \hfill 8.4726\end{array}$ c) $\begin{array}{ccccccc}\hfill t& \hfill 0& \hfill 1& \hfill 2& \hfill 5& \hfill 7& \hfill 10\\ \hfill P& \hfill 250& \hfill 125& \hfill 67.5& \hfill 38.75& \hfill 19.875& \hfill 9.9675\end{array}$ d) $\begin{array}{ccccccc}\hfill t& \hfill 0& \hfill 1& \hfill 2& \hfill 3& \hfill 4& \hfill 5\\ \hfill P& \hfill 12& \hfill 10& \hfill 8& \hfill 6& \hfill 4& \hfill 2\end{array}$ e) $\begin{array}{ccccccc}\hfill t& \hfill 0& \hfill 1& \hfill 2& \hfill 3& \hfill 4& \hfill 5\\ \hfill P& \hfill 20& \hfill 24& \hfill 28.8& \hfill 34.56& \hfill 41.472& \hfill 49.7664\end{array}$

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 $\frac{300}{147}=\frac{147}{72.03}=\dots =\frac{17.2944}{8.4726}\approx 2.04$ 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 $\frac{20}{24}=\frac{24}{28.8}=\dots =\frac{41.472}{49.7664}\approx 8.333$ are fixed so the function is exponential.
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 $\frac{300}{147}=\frac{147}{72.03}=\dots =\frac{17.2944}{8.4726}\approx 2.04$ 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 $\frac{20}{24}=\frac{24}{28.8}=\dots =\frac{41.472}{49.7664}\approx 8.333$ are fixed so the function is exponential.
Which of the following curves are concave up?
More than one answer may be correct.
 a) b) c) d)

There is at least one mistake.
For example, choice (a) should be True.
This curveis $y={e}^{x}$ 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.
Thiscurve 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.
Correct!
1. True This curveis $y={e}^{x}$ and it is concave up.
2. False Try again, this curve is concave down.
3. True Thiscurve is a quadratic and is concave up.
4. True This curve is$y={e}^{-x}$ and is concave up.
Consider the exponential function below and determine which one of the following statements is true.
$P\left(t\right)=800{\left(0.7\right)}^{t}$
 a) $P$ describes exponential growth where the initial quantity is $800\phantom{\rule{0.3em}{0ex}}.$ b) $P$ describes exponential decay where the initial quantity is $800\phantom{\rule{0.3em}{0ex}}.$ c) $P$ describes exponential growth where the initial quantity is $0.7\phantom{\rule{0.3em}{0ex}}.$ d) $P$ describes exponential decay where the initial quantity is $0.7\phantom{\rule{0.3em}{0ex}}.$

Choice (a) is incorrect
Try again, the factor by which $P$ changes is $0.7\phantom{\rule{0.3em}{0ex}}.$
Choice (b) is correct!
Choice (c) is incorrect
Try again, read the definition of The General Exponential Function on page 11.
Choice (d) is incorrect
Try again, read the definition of The General Exponential Function on page 11.
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

Choice (a) is incorrect
Try again, you have doubled the quantity twice.
Choice (b) is incorrect
Try again, this is how much you would have after 1620 years.
Choice (c) 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.
Choice (d) is incorrect
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.