a) \(\displaystyle{y}-{13.29}{\left({1.154}\right)}^{{x}}\)

b) take the integral of \(\displaystyle{\left({13.29}{\left({1.154}\right)}^{{{x}}}-{6}-{13.9}{e}^{{{.14}{x}}}\right.}\) from 20 to 25. Result: 18.427

Question

2021-06-14

a) \(\displaystyle{y}-{13.29}{\left({1.154}\right)}^{{x}}\)

b) take the integral of \(\displaystyle{\left({13.29}{\left({1.154}\right)}^{{{x}}}-{6}-{13.9}{e}^{{{.14}{x}}}\right.}\) from 20 to 25. Result: 18.427

asked 2021-08-13

The table shows the annual service revenues R1 in billions of dollars for the cellular telephone industry for the years 2000 through 2006.

\(\begin{matrix}
Year&2000&2001&2002&2003&2004&2005&2006\\
R_1&52.5&65.3&76.5&87.6&102.1&113.5&125.5
\end{matrix}\)

(a) Use the regression capabilities of a graphing utility to find an exponential model for the data. Let t represent the year, with t=10 corresponding to 2000. Use the graphing utility to plot the data and graph the model in the same viewing window.

(b) A financial consultant believes that a model for service revenues for the years 2010 through 2015 is \(\displaystyle{R}{2}={6}+{13}+{13},{9}^{{0.14}}{t}\). What is the difference in total service revenues between the two models for the years 2010 through 2015?

asked 2021-08-14

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

(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.

asked 2021-06-23

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.

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

(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.

asked 2021-06-10

The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006. Canada A=33.1e0.009t Uganda A=28.2e0.034t
Use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The models indicate that in 2013, Uganda's population will exceed Canada's.