Regents Exam: Algebra I August 2016 (Problem 24 of 37)

The video tutorial explains how to analyze an investment problem using an exponential function. It describes the function v(x) = 30,000 * 0.78^x, where x is the number of years since the investment was made. The tutorial identifies the function as an exponential decay model, with a base of 0.78 indicating a 22% annual decrease in value. The video guides viewers through eliminating incorrect options and solving for the rate of decay, concluding that the portfolio decreases by 22% per year.

What is the initial value of Milton's investment portfolio?

• $35,000

• $30,000

• $25,000

• $20,000

Which of the following best describes an exponential function?

• A function where the rate of change is proportional to its current value

• A linear function with a constant rate of change

• A function with a constant value over time

• A quadratic function with a variable rate of change

What does a base value between 0 and 1 in an exponential function indicate?

• Linear decay

• Linear growth

• Exponential decay

• Exponential growth

If the base of an exponential function is 0.78, what is the rate of decay?

• 22%

• 18%

• 28%

• 78%

Which option correctly describes the change in Milton's portfolio value over time?

• The portfolio decreases by 78% each year

• The portfolio decreases by 22% each year

• The portfolio increases by 78% each year

• The portfolio increases by 22% each year