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

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
Yes 7 14 21
No 12 7 19
Total 19 21 40
Find the conditional relative frequency that a student likes to lift weights, given that the student likes aerobics.

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?

Solve the given problem related to population growth.
During the first decade of this century the population of a certain city grew exponentially the population of the city was 146210 in 2000 and 217245 in 2010. Find the exponential growth function that models the population growth of the city use t= 0 to represent 2000 and t= 10 to represent 2010 and so on.
N(t)=?
Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.

The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006.
Canada
${\displaystyle A=33.1e^{0.009}t}$ Uganda ${\displaystyle A=28.2e^{0.034}t}$
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. Uganda's growth rate is approximately 3.8 times that of Canada's.

What function models exponential decay?
A. ${\displaystyle y=-3{\left(\frac{1}{2}\right)}^x}$
B. ${\displaystyle y=-\left(\frac{1}{2}\right){\left(3\right)}^x}$
C. ${\displaystyle y=\left(\frac{1}{2}\right){\left(3\right)}^x}$
D. ${\displaystyle y=3{\left(\frac{1}{2}\right)}^x}$