Exploring Exponential Growth and Decay Concepts

This video tutorial covers exponential growth and decay, explaining the formulas and providing examples. It starts with exponential growth, using investment and tuition examples to demonstrate how to calculate future values. The video then shifts to exponential decay, illustrating the concept with population and car value examples. Key concepts include converting percentages to decimals and applying the formulas to real-world scenarios.

What does the 'a' in the exponential growth formula represent?

• Growth rate

• Initial amount

• Time

• Final amount

How do you convert a growth rate from a percentage to a decimal?

• Multiply by 100

• Divide by 100

• Add 1

• Subtract 1

What is the formula for exponential growth?

• y = a - rt

• y = a(1 + r)^t

• y = a(1 - r)^t

• y = a + rt

After how many years was the tuition cost calculated in the example?

• 7 years

• 25 years

• 5 years

• 4 years

What is the formula for exponential decay?

• y = a(1 + r)^t

• y = a - rt

• y = a(1 - r)^t

• y = a + rt

In the exponential decay example, what was the rate of decay for the town's population?

• 8%

• 1%

• 12%

• 2.5%

How do you calculate the time period for the population example in exponential decay?

• 2008 - 2000

• 2015 - 2000

• 2015 - 2008

• 2000 - 2008

What was the initial value of the car in the depreciation example?

• $12,000

• $50,000

• $18,000

• $1,400

For the tractor depreciation example, what was the annual rate of depreciation?

• 8%

• 10%

• 12%

• 6%

What was the expected population in 2015 for the town decreasing at a rate of 2.5% per year?

• 28,000

• Less than 28,000

• More than 28,000

• Cannot be determined