Population Growth and Derivatives

The video tutorial explains how to model the population growth of Phoenix, Arizona, using an exponential function. It starts by establishing the initial population in 2000 and a growth rate of 3.4% per year. The tutorial then derives the exponential function and calculates the derivative to find the rate of population increase. Finally, it demonstrates how to calculate the population growth rate in 2020 using a scientific calculator.

What was the initial population of Phoenix, Arizona in the year 2000?

• 3,500

• 2,923

• 2,500

• 3,000

What is the annual growth rate expressed as a decimal?

• 3.4

• 0.0034

• 0.034

• 0.34

Which of the following represents the base of the exponential function for population growth?

• 1.034

• 1.34

• 0.034

• 3.4

What is the derivative of an exponential function with base 'a' with respect to its exponent?

• a^x

• a * ln(x)

• ln(a) * a^x

• x * a^x

In the context of this problem, what does the derivative function P' of T represent?

• The growth rate

• The total population

• The rate of population increase

• The initial population

How many years after 2000 is the year 2020?

• 15 years

• 25 years

• 20 years

• 10 years

What is the derivative function value P' of 20 used to calculate?

• The population in 2020

• The rate of population increase in 2020

• The initial population

• The growth rate in 2020

Which tool is used to calculate the exact rate of population increase?

• Spreadsheet software

• Basic calculator

• Desmos scientific calculator

• Graphing calculator

What is the rounded rate of population increase in 2020?

• 19,700

• 19,738

• 19,800

• 19,731

What is the unit for the rate of population increase calculated?

• People per year

• People per century

• People per decade

• People per month