Exponential Population Growth Analysis

The video tutorial explains how to model a city's population growth using an exponential function. Starting with a population of 500,000 in 2005 and 760,000 in 2010, the tutorial derives the exponential growth rate and function. It then uses this function to predict the population in 2025 and determine when the population will reach 1,000,000. The process involves solving exponential equations and applying logarithmic properties.

What was the population of the city in 2005?

• 500,000

• 760,000

• 1,000,000

• 2,668,971

What is the population of the city in 2010?

• 500,000

• 760,000

• 1,000,000

• 2,668,971

What is the base year used for the exponential growth model?

• 2025

• 2010

• 2005

• 2000

What is the formula used to calculate the exponential growth rate (K)?

• K = ln(1.52) / 5

• K = ln(760,000) / 500,000

• K = ln(2) / 5

• K = ln(500,000) / 760,000

What is the exponential function derived to model the population?

• P(t) = 500,000 * e^(0.083742 * t)

• P(t) = 500,000 * e^(0.1 * t)

• P(t) = 1,000,000 * e^(0.083742 * t)

• P(t) = 760,000 * e^(0.083742 * t)

How many years after 2005 is the population predicted for 2025?

• 20 years

• 30 years

• 15 years

• 25 years

What is the predicted population of the city in 2025?

• 500,000

• 760,000

• 1,000,000

• 2,668,971

What equation is used to find the year when the population reaches 1,000,000?

• 1,000,000 = 500,000 * e^(0.083742 * t)

• 1,000,000 = 500,000 * e^(0.1 * t)

• 1,000,000 = 760,000 * e^(0.083742 * t)

• 1,000,000 = 760,000 * e^(0.1 * t)

Approximately how many years after 2005 will the population reach 1,000,000?

• 15 years

• 10 years

• 8.28 years

• 5 years

In which year is the population expected to reach 1,000,000?

• 2020

• 2015

• 2013

• 2010