Exponential Functions and Models

This video tutorial explains how to analyze and manipulate exponential models to reveal hidden information using the properties of exponents. It covers the basics of exponential functions, their graphical representations, and how to calculate percent changes. The tutorial also demonstrates converting models to different time units and provides practical examples, such as car depreciation and population growth, to illustrate exponential growth and decay.

What is the characteristic of an exponential function when the base 'b' is greater than one?

• The function is constant.

• The function is linear.

• The function represents exponential growth.

• The function represents exponential decay.

What happens to the value of an exponential function when the base is between zero and one?

• The function represents exponential growth.

• The function represents exponential decay.

• The function becomes constant.

• The function becomes linear.

In an exponential model, what does the initial value represent?

• The horizontal asymptote.

• The y-intercept of the graph.

• The rate of change.

• The slope of the line.

What is the significance of the base in an exponential model?

• It determines the initial value.

• It indicates the rate of growth or decay.

• It is irrelevant to the model.

• It represents the horizontal asymptote.

How can you express an exponential model to highlight the percentage of change?

• By using a quadratic equation.

• By using a logarithmic equation.

• By using a linear equation.

• By writing the model in a form that includes the percentage of change.

What is the effect of changing the compounding interval from hourly to minute-based in an exponential model?

• It eliminates the need for a base.

• It makes the equation linear.

• It changes the organization of the equation but not the overall value.

• It changes the overall value of the equation.

How can you adjust an exponential model to show the percent of increase per minute?

• By dividing the hourly rate by 60.

• By multiplying the hourly rate by 60.

• By using the reciprocal of 60 in the exponent.

• By adding 60 to the base.

In the context of car depreciation, what does a base less than one indicate?

• The car's value is constant.

• The car's value is unpredictable.

• The car's value is decreasing.

• The car's value is increasing.

What is the result of compounding 365 times a year in a car depreciation model?

• The car's value remains the same.

• The car's value increases by 10% per year.

• The car's value increases by 0.03% per day.

• The car's value decreases by 0.03% per day.

How can you determine the daily percentage change from a weekly model?

• By using a linear approximation.

• By multiplying the weekly percentage by 7.

• By using the properties of exponents to adjust the model.

• By dividing the weekly percentage by 7.