Exponential Functions and Population Growth

This video tutorial covers exponential functions, explaining their form and properties, such as initial value, growth factor, and decay factor. It illustrates exponential growth and decay graphically and applies these concepts to model population growth. The tutorial also demonstrates solving exponential equations using graphical methods and logarithms.

What is the form of an exponential function?

• F(x) = A - B^X

• F(x) = A / B^X

• F(x) = A * B^X

• F(x) = A + B^X

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CCSS.HSF-IF.C.8B

What happens to the function values in exponential growth?

• They decrease at a constant rate.

• They remain constant.

• They fluctuate randomly.

• They increase at a constant percentage.

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CCSS.HSF-IF.C.8B

In exponential decay, what is the range of the base B?

• B < 0

• 0 < B < 1

• B = 1

• B > 1

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CCSS.HSF-LE.A.1B

What is the initial value of the population in the given example?

• 650

• 6,500

• 65

• 65,000

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CCSS.HSF-IF.C.8B

How is the growth rate represented in the exponential function for population?

• As a percentage

• As a fraction

• As a whole number

• As a decimal

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CCSS.HSF.LE.A.2

What is the predicted population in 2017 according to the model?

• 83,000

• 85,000

• 84,962

• 84,600

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CCSS.HSF-IF.C.7E

How do you determine the year when the population reaches 100,000?

• By using a ruler

• By using a graphing calculator

• By using a protractor

• By guessing

What mathematical tool is used to solve the exponential equation algebraically?

• Logarithms

• Addition

• Subtraction

• Multiplication

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CCSS.HSF.LE.A.4

What is the approximate value of T when the population reaches 100,000?

• 12.5

• 11.26

• 10.5

• 13.26

In which year is the population expected to reach 100,000?

• 2022

• 2021

• 2020

• 2023