Writing Exponential Equations from Data

The video tutorial explains how to write equations for exponential functions using tables and graphs. It covers the basic form of exponential equations, identifying initial values and common ratios, and determining whether a function represents growth or decay. The tutorial provides examples of writing equations from both tables and graphs, illustrating the process for both exponential growth and decay.

What does the 'a' value in an exponential function represent?

• The base of the natural logarithm

• The initial value or y-intercept

• The variable exponent

• The common ratio

If 'b' is greater than 1 in an exponential function, what does it indicate?

• Exponential decay

• Linear growth

• No growth

• Exponential growth

How do you find the 'a' value from a table?

• By multiplying the first y-value by the common ratio

• By finding the value when x equals 0

• By dividing any y-value by 2

• By finding the value when x equals 1

What is the common ratio if the y-values in a table are 3, 12, 48, 192?

• 4

• 3

• 48

• 12

In an exponential decay function, what would the 'b' value be likely to be?

• Less than 1

• Greater than 1

• Equal to 1

• Equal to 0

How can you determine the 'b' value for exponential decay from a table?

• By subtracting the smallest y-value from the largest

• By adding the y-values together

• By dividing a y-value by the preceding y-value

• By multiplying the y-values

What does a graph showing exponential decay look like?

• It forms a straight line

• It goes downwards from left to right

• It remains constant

• It goes upwards from left to right

How do you find the 'a' value from a graph?

• By finding where the graph crosses the x-axis

• By calculating the slope of the graph

• By finding where the graph crosses the y-axis

• By finding the highest point on the graph

What indicates exponential growth in a graph?

• The line moves downwards

• The line is straight

• The line forms a circle

• The line moves upwards

How is the 'b' value related to the points on a graph?

• It is determined by dividing one y-value by the previous y-value

• It is the sum of all x-values

• It is the difference between any two y-values

• It is the average of all y-values