The exponential growth models describe the population of the indicated country,

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.

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.

$\begin{array}{|cccccc|}\hline x& -1& 0& 1& 2& 3\\ g(x)& 2& 5& 8& 11& 14\\ \hline\end{array}$

Let V denote rainfall volume and W denote runoff volume (both in mm). According to the article “Runoff Quality Analysis of Urban Catchments with Analytical Probability Models” (J. of Water Resource Planning and Management, 2006: 4–14), the runoff volume will be 0 if ${\displaystyle [V\le v_d]}$ and will ${\displaystyle [k(V-v_d)\text{if}V>v_d.Here{v}_d]}$ is the volume of depression storage (a constant) and k (also a constant) is the runoff coefficient. The cited article proposes an exponential distribution with parameter ${\displaystyle [\lambda f\text{or}V.]}$
a. Obtain an expression for the cdf of W.
[Note: W is neither purely continuous nor purely discrete, instead it has a “mixed” distribution with a discrete component at 0 and is continuous for values ${\displaystyle w>0}$.]
b. What is the pdf of W for ${\displaystyle w>0}$? Use this to obtain an expression for the expected value of runoff volume.

The number of users on a website has grown exponentially since its launch. After 2 months, there were 300 users. After 4 months there were 30000 users. Find the exponential function that models the number of users x months after the website was launched.

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?

A computer valued at $1500 loses 20% of its value each year. a. Write a function rule that models the value of the computer. b. Find the value of the computer after 3 yr. c. In how many years will the value of the computer be less than $500? Remember the general form of an exponential function: $f(x)=a\ast b^x$. Given your table and situation, determine values for a and b. Write the appropriate exponential function.