Exponential Decay and Growth Concepts

This video tutorial covers exponential decay and its real-life applications. It explains the exponential function used for modeling decay, emphasizing the importance of converting rates to decimals. The tutorial includes two examples: the depreciation of a computer and the decline of an endangered bird population. It also provides guidance on using a calculator for exponential calculations. The video concludes with a call to action for viewers to engage with the content.

What is the formula for exponential decay?

• y = a * (1 + r)^x

• y = a * (1 - r)^x

• y = a * r^x

• y = a * x^r

In the context of exponential decay, what does 'a' represent in the formula y = a * (1 - r)^x?

• The initial amount

• The final amount

• The time in years

• The decay rate

How do you convert a percentage rate to a decimal for use in exponential decay calculations?

• Divide by 10

• Add 1 to the percentage

• Multiply by 100

• Divide by 100

What is the value of 2 to the power of 3?

• 8

• 6

• 9

• 12

If a computer worth $6500 depreciates at 14.3% per year, what is the value after 3 years?

• $6000.00

• $3500.00

• $5000.00

• $4091.25

What is the decay factor for a 14.3% depreciation rate?

• 0.714

• 1.143

• 0.143

• 0.857

How many birds will remain after 100 years if the population decreases at 0.75% annually from 200,000?

• 100,000

• 150,000

• 94,206

• 50,000

What is the decay factor for a 0.75% annual decrease?

• 1.0075

• 0.0075

• 0.9925

• 0.925

What is the initial bird population in the given problem?

• 250,000

• 150,000

• 200,000

• 100,000

What action is encouraged at the end of the video?

• Share the video

• Subscribe to the channel

• Dislike the video

• Ignore the content