Chicago Population Exponential Decay

The video tutorial explains how to model the declining population of Chicago using an exponential function. Starting with a population of 2.7 million in 2010, the population is decreasing at a rate of 7% per year. The exponential function is set up with the initial amount and decay rate, and the video demonstrates how to predict the population in 2030. The calculation shows that if the decline continues, the population will be approximately 0.63 million by 2030.

What was the population of Chicago in 2010?

• 2.5 million

• 3.0 million

• 2.7 million

• 3.5 million

At what rate is Chicago's population declining each year?

• 3 percent

• 5 percent

• 10 percent

• 7 percent

In the exponential function f(x) = a * b^x, what does 'a' represent?

• The initial amount

• The exponent

• The decay rate

• The base

What is the base 'b' in the exponential function for a declining population?

• r

• 1 - r

• 1

• 1 + r

How is the decay rate of 7% expressed as a decimal?

• 0.07

• 0.7

• -0.7

• -0.07

What is the simplified base of the exponential function for Chicago's population?

• 1.07

• 0.07

• 1.93

• 0.93

How many years after 2010 is the population prediction being made for?

• 10 years

• 15 years

• 20 years

• 25 years

What is the predicted population of Chicago in 2030?

• 0.63 million

• 1.63 million

• 3.63 million

• 2.63 million

What is the purpose of using an exponential function in this context?

• To model linear growth

• To model constant population

• To model exponential decay

• To model exponential growth

What is the significance of the year 2030 in this model?

• It is the year of minimum population

• It is the year of maximum population

• It is the base year

• It is the prediction year