Sketch a graph of the function. Use transformations of functions whenever possible. f(x)=1-2x

The exponential models describe the population of the indicated country, A, in millions, t years after 2010.Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
India, $A=1173.1e^{0.008t}$
Iraq, $A=31.5e^{0.019t}$
Japan, $A=127.3e^{0.006t}$
Russia, $A=141.9e^{0.005t}$

The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume that the population grows exponentially.
(a) Find a function that models the population t years after 1990.
(b) Find the time required for the population to double.
(c) Use the function from part (a) to predict the population of California in the year 2010. Look up California’s actual population in 2010, and compare.

The table shows the mid-year populations an of China (in millions) from 2002 through 2008. Year Population, an
___________________________
2002 1284.3
2003 1291.5
2004 1298.8
2005 1306.3
2006 1314.0
2007 1321.9
2008 1330.0 ___________________________ Use the exponential regression feature of a graphing utility to find a geometric sequence that models the data. Let n represent the year, with n=2 corresponding to 2002.

The populations P (in thousands) of Luxembourg for the years 1999 through 2013 are shown in the table, where t represents the year, with $t=9$ corresponding to 1999.

$\begin{array}{|lc|}\hline \text{ Year }& \text{ Population, }P\\ 1999& 427.4\\ 2000& 433.6\\ 2001& 439.0\\ 2002& 444.1\\ 2003& 448.3\\ 2004& 455.0\\ 2005& 461.2\\ 2006& 469.1\\ 2007& 476.2\\ 2008& 483.8\\ 2009& 493.5\\ 2010& 502.1\\ 2011& 511.8\\ 2012& 524.9\\ 2013& 537.0\\ \hline\end{array}$

(a) Use the regression feature of a graphing utility to find a linear model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (b) Use the regression feature of the graphing utility to find a power model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (c) Use the regression feature of the graphing utility to find an exponential model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (d) Use the regression feature of the graphing utility to find a logarithmic model for the data and to identify the coefficient of determination. Plot the model and the data in the same viewing window. (e) Which model is the best fit for the data? Explain. (f) Use each model to predict the populations of Luxembourg for the years 2014 through 2018. (g) Which model is the best choice for predicting the future population of Luxembourg? Explain. (h) Were your choices of models the same for parts (e) and (g)? If not, explain why your choices were different.

The table gives the midyear population of Japan, in thousands, from 1960 to 2010.
$\begin{array}{|cc|}\hline \text{Year}& \text{Population}\\ 1960& 94.092\\ 1965& 98.883\\ 1970& 104.345\\ 1975& 111.573\\ 1980& 116.807\\ 1985& 120.754\\ 1990& 123.537\\ 1995& 125.327\\ 2000& 126.776\\ 2005& 127.715\\ 2010& 127.579\\ \hline\end{array}$
Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. [Hint: Subtract 94,000 from each of the population figures. Then, after obtaining a model from your calculator, add 94,000 to get your final model. It might be helpful to choose $t=0$ to correspond to 1960 or 1980.]

The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. (If an answer does not exist, enter DNE.)
$\begin{array}{|llllll|}\hline x& -2& -1& 0& 1& 2\\ f(x)& 2& 4& 8& 16& 32\\ g(x)& 7& 0& 1& 0& 7\\ \hline\end{array}$

The popularity of fads and fashions often decays exponentially. One example is ticket sales for a popular movie. The table shows the total money spent per weekend on tickets in the United States and Canada for the movie The Da Vinci Code. $$$$\begin{array}{cc}\text{Weekend in 2006}& TicketSales(millions)\\ \text{May 19—May 21}& \text{77.1}\\ \text{May 26—May 28}& \text{34.0}\\ \text{June 2—June 4}& \text{18.6}\\ \text{June 9—June 11}& \text{10.4}\\ \text{June 16—June 18}& \text{5.3}\\ \text{June 23—June 25}& \text{4.1}\\ \text{June 30—July 2}& \text{2.3}\end{array}$$$ a) Use a graphing calculator to create a scatter plot of the data. b) Draw a quadratic curve of best fit. - Press STAT, cursor over to display the CALC menu, and select 5:QuadReg. - Press VARS, and cursor over to display the Y-VARS menu. Select 1:Function and then select 1:Y1. - Press ENTER to get the QuadReg screen, and press GRAPH. c) Draw an exponential curve of best fit. - Press STAT, cursor over to display the CALC menu, and select 0:ExpReg. - Press VARS, and cursor over to display the Y-VARS menu. Select 1:Function and then select 2:Y2. - Press ENTER to get the ExpReg screen, and press GRAPH. d) Examine the two curves. Which curve of best fit best models the data?