Exploring Exponential Growth: Determining Population

This lesson covers the determination of population using exponential models. It begins with an introduction to exponential expressions, explaining the roles of the base and exponent. The lesson then clarifies the difference between independent and dependent variables, using real-world examples. A detailed example of population growth is provided, illustrating how to calculate population over time using exponential functions. The lesson concludes with a demonstration of graphing and algebraic methods to estimate and calculate population at various time intervals.

What are the two main components of an exponential expression?

• Variable and constant

• Base and exponent

• Root and power

• Exponent and coefficient

What is the result of any non-zero number raised to the power of zero?

• Zero

• The number itself

• Infinity

• One

How should you input an expression like 25 to the one-half power into a calculator to get the correct result?

• (25^1)/2

• 25/2

• 25^(1/2)

• 25^1/2

In a word problem, what is typically the independent variable?

• The output or result

• The variable that changes based on another

• The input or cause

• The constant value

In the population growth problem, what is the independent variable?

• Years

• Initial population

• Growth rate

• Population size

What is the population of the town after 50 years, according to the exponential model?

• 8,500

• 9,000

• 10,000

• 9,352

How can you find the population after any number of years using the exponential model?

• By using a fixed growth rate

• By estimating from a graph

• By substituting the number of years into the function

• By calculating manually each year