Find Expontntial Model that fits the points shown in the graph of table01510102841.jpg

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 exponential models describe the population of the indicated country. A, in millions, t years after 2006. Which country has the greates growth rate? By what percentage is the population of that country increasing each year?
Country1: ${\displaystyle A=129.3e^{0.001t}}$
Country 2: ${\displaystyle A=1096.9e^{0.011t}}$
Country 3: ${\displaystyle A=28.7e^{0.028t}}$
Country 3: ${\displaystyle A=147.9e^{-0.004t}}$

Use the exponential growth model $A=A_0{e}^{kt}$ to solve: In 2000, there were 110 million cellphone subscribers in the United States. By 2010, there were 303 million subscribers
a. Find the exponential function that models the data.
b. According to the model, in which year were there 400 million cellphone subscribers in the United States?

The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table. $\begin{array}{|cccccccc|}\hline \text{Year}& 2004& 2005& 2006& 2007& 2008& 2009& 2010\\ \text{Sales, S}& 898.2& 1024.1& 1366.8& 1447.4& 1822.1& 2006.9& 2268.9\\ \hline\end{array}$

a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t=4 corresponding to 2004. b) Use the regression feature of the graphing utility to find an exponential model for the data. Use the Inverse Property $b=e^{\ln b}$to rewrite the model as an exponential model in base e. c) Use the regression feature of the graphing utility to find a logarithmic model for the data. d) Use the exponential model in base e and the logarithmic model to predict sales in 2011. It is projected that sales in 2011 will be $2740 million. Do the predictions from the two models agree with this projection? Explain.

 

With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?

Show that an exponential model fits the data. Then write a recursive rule that models the data.
n 0 1 2 3 4 5 f(n)96 54 48 24 12 6 3 ​