Compound Growth and Decay: Understanding the Formula and Real-World Applications

The video tutorial explains compound growth and decay, using real-world examples like interest, bacteria growth, and depreciation. It introduces the formula for calculating compound interest and demonstrates its application through examples. The tutorial also covers the iterative method for growth calculation and how to rearrange the formula to find initial investments.

Which of the following is an example of compound decay?

• Bacteria multiplying in a Petri dish

• A loan accruing interest

• A car losing value over time

• Interest earned on a savings account

What is the multiplier used for a 5% annual increase?

• 1.15

• 0.95

• 1.5

• 1.05

How can the compound interest calculation be simplified using indices?

• By multiplying the principal by the rate for each year

• By adding the rate to the principal each year

• By using the rate to the power of the number of years

• By subtracting the rate from the principal each year

What is the formula for calculating compound decay?

• Principal times (1 + rate) to the power of years

• Principal times (1 - rate) to the power of years

• Principal divided by (1 + rate) to the power of years

• Principal divided by (1 - rate) to the power of years

If a car depreciates by 15% annually, what is the multiplier used?

• 1.5

• 0.85

• 0.15

• 1.15

How many hours does it take for 400 bacteria cells to exceed 750 if they grow by 15% each hour?

• 5 hours

• 4 hours

• 3 hours

• 6 hours

What is the initial investment if the final amount is £10,775.14 after 12 years at a 5% annual interest rate?

• £8,000

• £6,000

• £7,000

• £5,000