Exploring Exponential Growth and Decay Functions

The video tutorial covers exponential growth and decay, explaining their formulas and graphing techniques. It discusses the concept of horizontal asymptotes and how they affect the graph. The tutorial also introduces exponential models used for real-life applications, such as calculating the value of a car over time. Finally, it explains compound interest, detailing how to calculate it using a specific formula.

What is the condition for a function to show exponential growth?

• The exponent must be negative.

• The base number must be less than one.

• The coefficient must be negative.

• The base number must be greater than one.

What is the formula for exponential growth?

• y = a(1 + r)^t

• y = ab^x

• y = a/b^x

• y = a(1 - r)^t

What does the horizontal asymptote in an exponential function represent?

• The minimum value of the function.

• The maximum value the function can reach.

• A boundary the function's graph never crosses.

• The point where the function starts to decrease.

What does the term 'domain' refer to in an exponential function?

• The slope of the function.

• The set of all possible y-values.

• The set of all possible x-values.

• The maximum value of the function.

What is a key characteristic of exponential decay?

• The function's value increases over time.

• The base of the function's formula is between 0 and 1.

• The graph of the function crosses the x-axis.

• The function's rate of change is constant.

In the context of exponential decay, what does a base value between 0 and 1 indicate?

• The function will decrease over time.

• The function will oscillate.

• The function will increase indefinitely.

• The function will remain constant.

How is the annual percent decrease calculated in an exponential decay model?

• By subtracting the base from 1 and converting to a percentage.

• By adding the base to 1 and converting to a percentage.

• By dividing the base by 1 and converting to a percentage.

• By multiplying the base by 100.

What does the 'r' represent in the exponential growth and decay formulas?

• The total number of units.

• The initial amount or value.

• The rate of growth or decay per unit.

• The base of the exponential function.

What does the 'P' represent in the compound interest formula?

• The principal or initial amount.

• The final amount after interest.

• The annual interest rate.

• The number of times interest is compounded per year.

How often is interest compounded in a quarterly compounded interest account?

• Twelve times a year

• Once a year

• Four times a year

• Twice a year