A population consists of these values: 2, 3, 6, 8, 11, 18.

The data on the right represent the world population. An ecologist is interested in building a model that describes the world population.

$$\begin{array}{|cccc|} \hline \text { Year } & \begin{array}{c} \text { Population } \\ \text { (billions) } \end{array} & \text { Year } & \begin{array}{c} \text { Population } \\ \text { (billions) } \end{array} \\ \hline 2001 & 6.17 & 2008 & 6.71 \\ \hline 2002 & 6.24 & 2009 & 6.79 \\ 2003 & 6.32 & 2010 & 6.87 \\ 2004 & 6.40 & 2011 & 6.94 \\ 2005 & 6.47 & 2012 & 7.02 \\ 2006 & 6.55 & 2013 & 7.10 \\ 2007 & 6.63 & 2014 & 7.18 \\ \hline \end{array}$$

Using a graphing utility, build a logistic model from the data.

Solve each problem. See Examples mentioned.

World population in millions closely fits the exponential function

$$f(x)=6084 e^{0.0120 x}$$

where x is the number of years since 2000. (Source: U.S. Census Bureau.)

(a) The world population was about 6853 million in 2010 . How closely does the function approximate this value?

(b) Use this model to predict world population in 2020 and 2030.

In 1862, it was discovered that cholesterol is converted into a new substance named coprostanol by the action of bacteria in the human digestive tract. Make use of the following information to deduce the structure of coprostanol. Identify the structures of unknowns J through M as well.

(i) Coprostanol, upon treatment with Cr(VI) reagents, gives compound J, UV: $\lambda_{\max }(\epsilon)=281(22) \mathrm{nm}$ and IR: $\tilde{v}=1710 \mathrm{~cm}^{-1}$.

(ii) Exposure of cholesterol to $\mathrm{H}_2$ over Pt results in compound K, a stereoisomer of coprostanol. Treatment of K with the Cr(VI) reagent furnishes compound L, which has a UV peak very similar to that of compound $\mathrm{J}, \lambda_{\max }(\epsilon)=258(23) \mathrm{nm}$, and turns out to be a stereoisomer of J.

(iii) Careful addition of Cr(VI) reagent to cholesterol produces M: UV: $\lambda_{\max }(\epsilon)=286(109) \mathrm{nm}$. Catalytic hydrogenation of M over Pt also gives L.

For an in-control process with subgroup data n=4, $\bar{X}$=20, and $\bar{R}$=2, find the estimate of

a. the population mean of all X values.

b. the population standard deviation of all X values.

In 2005, the population of Bay City was $19,611$. For each of the next five years, the population decreased by an average of $715$ people per year.a. What was the population in $2010$ ? b. If the population continues to decline at the same rate as from $2005$ to $2010$ , what would you expect the population to be in $2025$ ?

A Ferris wheel is In the shape of a clrcle. Recall that a circle is the set of all points in a plane that are equidistant from a given point, which is called the center of the circle. The distance from a point on the circle to the center is the radius of the circle. A circle is named by its center. For example, the circle seen in the Ferris wheel is circle $P$. Use the circle to answer each question. a. Name the circle. b. Use a straightedge to draw $\overline{O B}$, a radius of circle $O$. Where are the endpoints located with respect to the circle? c. How many radili does a circle have? Explain your reasoning. Remember, radii ts the plural of radius. d. Use a straightedge to draw $\overline{A C}$. Then, use a straightedge to draw $\overline{B D}$. How are the line segments different? How are they the same? oth line segments $A C$ and $B D$ are chords of the circle. A chord is a line segment with each Idpoint on the circle. Line segment $A C$ is called a diameter of the circle. A diameter is a ord that passes through the center of the circle. e. Why is $\overline{B D}$ not considered a diameter? f. How does the length of the diameter of a circle relate to the length of the radius? g. Are all radii of the same circle, or of congruent circles, always, sometimes, or never congruent? Explain your reasoning.

Table shows world population, $P$, in billions of people, world passenger automobile production, $A$, in millions of cars, and world cell phone subscribers, $C$, in millions of subscribers. ${ }^{33}$ (a) Find the average rate of change, with units, for each of $P, A$, and $C$ between 1995 and 2005 . (b) Between 1995 and 2005, which increased faster: (i) Population or the number of automobiles? (ii) Population or the number of cell phone subscribers?

$$\begin{array}{c|c|c|c} \hline \text { Year } & 1995 & 2000 & 2005 \\ \hline P \text { (billions) } & 5.68 & 6.07 & 6.45 \\ \hline A \text { (millions) } & 36.1 & 41.3 & 45.9 \\ \hline C \text { (millions) } & 91 & 740 & 2168 \\ \hline \end{array}$$

The population of the world reached 1 billion in 1804 , 2 billion in 1927,3 billion in 1960,4 billion in 1974,5 billion in 1987 and 6 billion in 1999 . Find the average rate of change of the population of the world, in people per minute, during each of these intervals (that is, from 1804 to 1927,1927 to 1960 , etc.).

The data on the right represent the world population. An ecologist is interested in building a model that describes the world population.

$$\begin{array}{|cccc|} \hline \text { Year } & \begin{array}{c} \text { Population } \\ \text { (billions) } \end{array} & \text { Year } & \begin{array}{c} \text { Population } \\ \text { (billions) } \end{array} \\ \hline 2001 & 6.17 & 2008 & 6.71 \\ \hline 2002 & 6.24 & 2009 & 6.79 \\ 2003 & 6.32 & 2010 & 6.87 \\ 2004 & 6.40 & 2011 & 6.94 \\ 2005 & 6.47 & 2012 & 7.02 \\ 2006 & 6.55 & 2013 & 7.10 \\ 2007 & 6.63 & 2014 & 7.18 \\ \hline \end{array}$$

When will world population be 10 billion?

State how can you choose values for x when making a table of values representing a real world situation.

You have just been named president of the famous perfume company, Scents "R" Us. Searching for a hot new item to market, you run across a bottle labeled only $\mathrm{C}_{10} \mathrm{H}_{20} \mathrm{O}$, which contains a liquid with a wonderfully sweet rose aroma. You want more, so you set out to elucidate its structure. Do so from the following data.

(i) ${ }^1 \mathrm{H} \mathrm{NMR}$ : clear signals at $\delta$ = 0.94 (d, J = 7 Hz, 3 H), 1.63 (s, 3 H), 1.71 (s, 3 H), 3.68 (t, J = 7 Hz, 2 H), 5.10 (t, J = 6 Hz, 1 H) ppm; the other 8 H have overlapping absorptions in the range $\delta$ = 1.3-2.2 ppm.

(ii) ${ }^{13} \mathrm{C}$ NMR $\left({ }^1 \mathrm{H}\right.$ decoupled): $\delta$ = 60.7, 125.0, 130.9 ppm; seven other signals are upfield of $\delta$ = 40 ppm.

(iii) IR: $\widetilde{\nu}=1640$ and $3350 \mathrm{~cm}^{-1}$.

(iv) Oxidation with buffered PCC gives a compound with the molecular formula $\mathrm{C}_{10} \mathrm{H}_{18} \mathrm{O}$. Its spectra show the following changes compared with the starting material: ${ }^1 \mathrm{H}$ NMR: signal at $\delta$ = 3.68 ppm is gone, but a new signal is seen at $\delta$ = 9.64 ppm; ${ }^{13} \mathrm{C}$ NMR: signal at $\delta$ = 60.7 ppm is gone, replaced by one at $\delta$ = 202.1 ppm; IR: loss of signal at $\widetilde{\nu}=3350 \mathrm{~cm}^{-1}$; new peak at $\widetilde{\nu}=1728 \mathrm{~cm}^{-1}$.

(v) Hydrogenation gives $\mathrm{C}_{10} \mathrm{H}_{22} \mathrm{O}$, indentical with that formed on hydrogenation of the natural product geraniol (see below).

A population consists of the following three values: 1, 2, and 3. a. List all possible samples of size 2 and compute the mean of every sample. b. Find the means of the distribution of the sample mean and the population mean. Compare the two values. c. Compare the dispersion of the population with that of the sample mean. d. Describe the shapes of the two distributions.

The compound whose structure is $\mathrm{H}-\mathrm{C} \equiv \mathrm{C}\left(\mathrm{CH}_2\right)_3 \mathrm{Cl}$ is best named (IUPAC)

(a) 4-chloro-1-pentyne;

(b) 5-chloropent-1-yne;

(c) 4-pentyne-1-chloroyne;

(d) 1-chloropent-4-yne.