Exponential Functions and Growth

The video tutorial explains exponential relationships, focusing on their rapid increase or decrease over time. It covers the general form of exponential functions, conditions for growth, and how to graph these functions. The tutorial also includes solving problems using tables, finding missing values, and matching graphs to equations. Key concepts include the initial value, growth factor, and the importance of equal factors over equal intervals.

What is the general form of an exponential function?

• y = a + b * x

• y = a * b^x

• y = a / b^x

• y = a - b * x

Under what conditions does exponential growth occur?

• a < 0 and b < 1

• a > 0 and b < 1

• a > 0 and b > 1

• a < 0 and b > 1

How do Y values behave in an exponential growth graph as X values increase?

• Y values increase rapidly

• Y values decrease rapidly

• Y values decrease slowly

• Y values remain constant

What is the initial value of an exponential function?

• The value of x when y = 1

• The value of x when y = 0

• The value of y when x = 0

• The value of y when x = 1

How do you find the growth factor 'b' in a table of exponential values?

• Subtract each Y value from the previous Y value

• Add each Y value to the previous Y value

• Multiply each Y value by the previous Y value

• Divide each Y value by the previous Y value

What is the value of y when x = 0 for the function y = 25 * 2^x?

• 25

• 50

• 1

• 0

If y = 25 * 2^x, what is y when x = 4?

• 200

• 100

• 800

• 400

For the equation y = 5 * 3^x, what is the initial value?

• 3

• 5

• 0

• 15

Which point should be on the graph of y = 5 * 3^x?

• (1, 5)

• (1, 3)

• (0, 5)

• (0, 3)

What is the y value when x = 1 for the function y = 5 * 3^x?

• 5

• 10

• 15

• 20