Exploring Rational Expressions in Algebra

The video tutorial covers the concepts of exponential growth and decay, explaining how to identify and model these functions. It provides examples of exponential growth, such as the increase in value of a coin, and exponential decay, like the depreciation of a boat's value. The tutorial also discusses how to graph these functions, determine their domain and range, and interpret the y-intercept. Additionally, it compares two exponential functions representing stock values, highlighting the differences in their growth and decay rates.

What indicates an exponential growth in the function y = a * b^x?

• b is less than 1

• b is 0

• b is exactly 1

• b is greater than 1

What does a rate greater than 1 in an exponential function indicate?

• Decay

• No change

• Growth

• Oscillation

What does the y-intercept represent in an exponential function?

• The slope of the function

• The initial or starting value

• The maximum value of the function

• The rate of growth or decay

How do you convert a percentage increase to a decimal for an exponential growth function?

• Divide by 100

• Multiply by 100

• Add to 1

• Subtract from 1

What is the significance of converting a percentage to a decimal in exponential functions?

• It increases the rate of growth or decay

• It simplifies the calculation

• It decreases the rate of growth or decay

• It is necessary for calculating the function's value

What is the domain of an exponential function representing time?

• x is less than 0

• x is greater than 0

• x is greater than or equal to 0

• All real numbers

In the context of exponential decay, what does a rate of 9% per year translate to in the function?

• 0.91

• 0.09

• 1.09

• -0.09

How do you determine the year to input into the function for calculating future value?

• Subtract the base year from the target year

• Use the current year

• Add the base year to the target year

• Use the target year directly

What does the range y is less than or equal to 17800 signify in an exponential decay function?

• The function has no lower limit

• The function starts at 17800 and decreases

• The function starts at 17800 and increases

• The function has no upper limit

What does an intersection point in the graph of two exponential functions represent?

• The point where their values are exactly the same

• The point where their rates of growth or decay are equal

• The point where their domains overlap

• The point where their initial values are equal