Exponential Functions and Value Changes

This video tutorial explains exponential functions, focusing on those with percentage increases or decreases. It covers the basic form of exponential functions, where 'a' is the initial value and 'B' is the growth rate. Two examples are provided: calculating credit card debt with a 15% annual interest rate and determining car depreciation with an 8% annual decrease. The video concludes with a summary of how to handle percentage changes in exponential functions.

What is the general form of an exponential function?

• y = a/x

• y = ax^2 + bx + c

• y = a * B^x

• y = mx + b

In an exponential function, what does the 'a' value represent?

• The y-intercept or initial value

• The x-intercept

• The slope

• The exponent

What is the role of the 'B' value in an exponential function?

• It determines the slope

• It is the initial value

• It is the growth rate

• It is the x-intercept

In the function y = 3 * 2^x, what does the number 2 represent?

• The y-intercept

• The x-intercept

• The growth rate

• The initial value

How do exponential functions with percentage changes differ from simple exponential functions?

• They use addition instead of multiplication

• They are linear functions

• They involve percentage increases or decreases

• They have a constant rate of change

If you have $500 in debt with a 15% annual interest, what is the initial value in the exponential function?

• $500

• $515

• $15

• $575

What is the correct growth rate to use for a 15% increase?

• 15

• 1.15

• 0.15

• 0.85

Why can't you use 0.15 as the growth rate for a 15% increase?

• It would imply a 150% increase

• It would imply retaining only 15% of the value

• It would imply a 15 times increase

• It would imply a 15% decrease

If a car depreciates by 8% annually, what is the correct growth rate to use?

• 0.92

• 0.08

• 1.92

• 1.08

What does a growth rate of 0.92 imply in terms of value retention?

• Increasing by 92%

• Retaining 8% of the value

• Increasing by 8%

• Retaining 92% of the value