Investment Growth and Exponential Functions

The video tutorial explains how to calculate the future value of an investment initially worth $10,000 under different growth scenarios using exponential functions. It covers three scenarios: growth by 5% annually, every 3 years, and every 6 months. The tutorial provides formulas for each scenario, compares the results, and verifies the correctness of the formulas through tables.

What is the initial value of the investment?

• $15,000

• $5,000

• $20,000

• $10,000

In the exponential growth formula, what does 'a' represent?

• Initial value

• Time period

• Growth rate

• Final value

How often does the investment grow in the first scenario?

• Every 6 months

• Every year

• Every 3 years

• Every 5 years

What is the exponent in the formula for annual growth?

• T/3

• T/2

• 2T

• T

In the second scenario, how often does the investment grow?

• Every 5 years

• Every 3 years

• Every 2 years

• Every year

What is the exponent in the formula for growth every 3 years?

• 3T

• T/3

• T/2

• T

In the third scenario, how often does the investment grow?

• Every year

• Every 2 years

• Every 3 months

• Every 6 months

What is the exponent in the formula for growth every 6 months?

• T/3

• 2T

• T

• T/2

After how many years does the investment reach $10,500 in the annual growth scenario?

• 2 years

• 3 years

• 1 year

• 6 months

In the comparison, which scenario reaches $10,500 the fastest?

• Annual growth

• Growth every 3 years

• Growth every 6 months

• None