When a < 0 and b>1,y=abx models negative exponential growth. a. Write an exponential function that models negative growth. b. Give an example of a situation that could be modeled by your function. c. Explain one difference between negative exponential growth and exponential decay.

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.

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
$\begin{array}{|ccccccccccc|}\hline x& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ f(x)& 20& 21.6& 29.2& 36.4& 46.6& 55.7& 72.6& 87.1& 107.2& 138.1\\ \hline\end{array}$

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 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?

Explain please

The government of a large city needs to determine whether the citys