Population Dynamics and Linear Functions

The video tutorial explains the linear decline in the population of a small town in Central Florida from 1992 to 2000. It demonstrates how to formulate a linear equation to express the population as a function of time, using ordered pairs to calculate the slope. The tutorial derives the equation and uses it to predict the population in 2004, showing a decrease of 510 people per year.

What was the population of the town in 1992?

• 44,200 people

• 40,120 people

• 50,000 people

• 42,000 people

In what form is a linear function typically expressed?

• f(x) = mx + b

• f(x) = a/x + b

• f(x) = x^2 + bx + c

• f(x) = ax^2 + bx + c

What is the ordered pair for the year 2000?

• (0, 40,120)

• (8, 40,120)

• (0, 44,200)

• (8, 44,200)

How do you calculate the slope (m) of a linear equation?

• Change in population divided by change in years

• Change in years divided by change in population

• Sum of population and years

• Difference between initial and final population

What is the slope (m) of the population decline equation?

• 400

• -510

• 510

• -400

What does a negative slope indicate in the context of population change?

• The population is stable

• The population is fluctuating

• The population is decreasing

• The population is increasing

What is the linear equation for the population decline?

• p(t) = 40,120 - 510t

• p(t) = 44,200 - 510t

• p(t) = 40,120 + 510t

• p(t) = 44,200 + 510t

How many years after 1992 is the year 2004?

• 12 years

• 14 years

• 8 years

• 10 years

What is the predicted population of the town in 2004?

• 38,080 people

• 40,120 people

• 44,200 people

• 36,000 people

What is the base year used for calculating t in the linear equation?

• 1992

• 2004

• 2000

• 1982