As with linear models, exponential models can increase, which is called exponential growth, or decrease, which is called exponential decay. You will see an example of exponential decay in Lesson 4.4.
Compound interest is one application of exponential growth. There are many others. The formula that you found for annual compound interest can be generalized to all exponential growth models:
New Value = Starting Value x (1 + rate)variable power
Populations often grow exponentially. Question 1 examines how you can use this to make predictions about the world population.
(1) Scientists use models to project population in the future. While these models have limitations, they help leaders plan ahead for the resources people will need. The World Bank estimates that that the world population growth rate in 2010 was 1.1%.
The U.S. Census Bureau estimated the world population in 2010 to be about 6.9 billion people.
(a) This is an exponential situation because the population is increasing each year by a percentage of the previous year. Complete the table below based on the growth rate of 1.1%. Some of the entries are done for you. Round your answer to the nearest hundredth.
Calendar Year Number of Years After 2010 Projected Population, billions
2010 0 6.90
2011 1
2012
2013
(b) Write an exponential equation for the world population growth after 2010. Let P = the projected population in billions and t = the number of years after 2010. Hint: Think about how you calculated the entries in the table. If you started with 6.9 billion each time, how could you calculate each population? Think back to your work in the lesson.
A. P=6.9(1+0.011)^t
B. P=6.9(1+0.011^t)
C. P=6.9(1-0.011 × t)
D. P=6.9(1+0.011 × t)
(c) Use your model to predict the population in 2020. Round your answer to the nearest hundredth.
billion people
