Population Growth and Exponential Functions

The video tutorial explains how to solve an application problem involving a geometric sequence. It focuses on calculating the projected population of a town that grows by 15% annually, starting with a population of 100,000 in 2010. The tutorial walks through the calculation process to find the population in 2020, using the formula for geometric sequences. The final result is approximately 400,000, which is presented as the answer.

What type of mathematical sequence is used to solve the population growth problem?

• Arithmetic sequence

• Geometric sequence

• Fibonacci sequence

• Harmonic sequence

What was the initial population of the town in 2010?

• 150,000

• 100,000

• 50,000

• 75,000

By what percentage does the town's population grow each year?

• 20%

• 10%

• 12%

• 15%

Over how many years is the population growth calculated?

• 8 years

• 12 years

• 5 years

• 10 years

What is the formula used to calculate the population in 2020?

• Initial population + (growth rate * years)

• Initial population * (1 + growth rate)^years

• Initial population * growth rate * years

• Initial population / (1 + growth rate)^years

What is the growth rate factor used in the calculation?

• 1.12

• 1.15

• 1.20

• 1.10

How is the growth rate factor applied each year in the calculation?

• It is added to the initial population each year.

• It is divided by the initial population each year.

• It is subtracted from the initial population each year.

• It is multiplied by the initial population each year.

What is the value of 1.15 raised to the power of 10?

• 404

• 504

• 604

• 304

What is the approximate projected population of the town in 2020?

• 450,000

• 400,000

• 350,000

• 300,000

Which option was selected as the correct answer for the projected population?

• Option B

• Option C

• Option D

• Option A