Exponential Growth and Decay Concepts

This video tutorial covers solving word problems involving exponential growth and decay. It begins with a review of the basic concepts and formulas, explaining how to identify and apply them. Two examples are provided: one on calculating the future value of a house with a constant growth rate, and another on determining the future population of an endangered bird species with a constant decay rate. The video encourages viewers to practice solving similar problems independently.

What is the general formula for exponential growth or decay?

• y = a - bx

• y = a / b^x

• y = a * b^x

• y = a + bx

In the context of exponential growth, what does the variable 'r' represent?

• The initial value

• The final value

• The growth rate

• The time period

If a house's value increases by 3% annually, which formula would you use to calculate its future value?

• y = a * (1 + r)^x

• y = a / (1 + r)^x

• y = a * b^x

• y = a * (1 - r)^x

What is the initial value of the house in the example problem?

• $200,000

• $250,000

• $300,000

• $350,000

How many years are considered in the house value example problem?

• 5 years

• 7 years

• 9 years

• 11 years

In the context of exponential decay, what does the variable 'r' represent?

• The initial value

• The final value

• The decay rate

• The time period

Which formula is used to calculate exponential decay?

• y = a / (1 - r)^x

• y = a * (1 + r)^x

• y = a * b^x

• y = a * (1 - r)^x

What is the initial population of the endangered bird in the example problem?

• 1,500

• 1,600

• 1,700

• 1,800

How many years are considered in the bird population example problem?

• 6 years

• 5 years

• 4 years

• 7 years

What is the decay rate of the bird population in the example problem?

• 1.0%

• 2.5%

• 1.5%

• 2.0%