Exploring Exponential Growth and Compound Interest

I'm learning about  geometry dash lite exponential growth and compound interest and would like a detailed explanation of the following multi-part problem.

Part A

A savings account starts with $1,000 and earns 5% interest per year.

• Calculate the account balance after 1 year.
• Calculate the balance after 2 years.
• Explain why the increase in the second year is larger than in the first year.

Part B

Now suppose the same account compounds interest monthly instead of annually.

• What is the monthly interest rate?
• Calculate the balance after 1 year.
• Compare the result with annual compounding.

Part C

A different investment starts with $2,500 and grows by 8% each year.

• Write an equation that models the investment value after (t) years.
• Calculate the value after 5 years.
• Explain how exponential growth differs from linear growth.

Part D

A population of bacteria doubles every 6 hours.

• If there are initially 500 bacteria, how many will there be after 24 hours?
• Show all calculations.
• Explain how doubling time affects growth speed.

Part E

Compare the following situations:

1. An account earning 4% annual interest.
2. An account earning 6% annual interest.
3. A population that doubles every year.

• Which grows the fastest over a long period?
• Explain your reasoning using the concept of exponential growth.
• Discuss how small differences in growth rates can lead to large differences over time.

Please provide step-by-step calculations and explanations for each part.