Use exponential regression to find a function that models the data.begin{array}{|c|c|} hline x & 1 & 2 & 3 & 4 & 5 hline f(x) & 14 & 7.1 & 3.4 & 1.8 & 0.8 hline end{array}

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

A report tells us that in 2009, there were 870 gray wolves in Idaho, but that the population declined by 19% annual rate of decrease continues.
a) Find an exponential model that gives the wolf population W as a function of the time t in years since 2009.
${\displaystyle W=870{(1-.19)}^t}$
b) It is expected that the wolf population cannot recover if there are fewer than 25 individuals. How long must this rate of decline continue for the wolf population to reach 25?

The table shows the number of employees at a software company in various years.
Years Since 2000 4 6 8 10 Number of Employees 32 40 75 124
Use your calculator to find an exponential equation that models the growth of the company.

The population of a small town was 3,600 people in the year 2015. The population increases by 4.5% every year.
Write the exponential equation that models the population of the town t years after 2015.
Then use your equation to estimate the population in the year 2025?

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.)
$\begin{array}{|llllll|}\hline x& -2& -1& 0& 1& 2\\ f(x)& 2& 4& 8& 16& 32\\ g(x)& 7& 0& 1& 0& 7\\ \hline\end{array}$

You invest $1000 at 7% interest compounded annually. What is the exponential equation that models this situation? According to your equation, how much will the investment be worth 3 years later?