Use the two-way table of data from another student survey to answer the following question. Like Aerobic Excercise Like Weight Lifting Yes No Total Ye

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 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, $A=141.9e^{0.005t}$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I’m using a photocopier to reduce an image over and over by 50%,so the exponential function ${\displaystyle f\left(x\right)={\left(\frac{1}{2}\right)}^x}$ models the new image size, where x is the number of reductions.

The initial value of car is $24,000. After one year the value of the car is $19,3550. What exponential dunction models the expected value of the car? Estimate the value of the car after 4 years.

Use Exponential Models in Applications
In the following exercises, solve.
Sayed deposits $20,000 in an investment account. What will be the value of his investment in 30 years if the investment is earning 7% per year and is compounded continuously?

The population of a region is growing exponentially. There were 10 million people in 1980 (when $t=0$) and 75 million people in 1990. Find an exponential model for the population (in millions of people) at any time tt, in years after 1980.
P(t)=?
What population do you predict for the year 2000?
Predicted population in the year 2000 =million people. What is the doubling time?

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.