Writing Exponential Functions from Various Sources

The video tutorial reviews different methods to represent exponential functions, starting with equations where 'a' is the initial value and 'b' is the growth or decay rate. It explains how to derive exponential functions from graphs by identifying the y-intercept and calculating the growth or decay rate using consecutive points. The tutorial also covers writing exponential functions from tables by identifying the y-intercept and common ratio. Finally, it applies these concepts to word problems, demonstrating how to match scenarios with the correct exponential equations.

What is the initial value (a) in the equation y = 4 * (2/3)^x?

• y

• x

• 4

• 2/3

In the equation y = 0.5 * (5/2)^x, what type of function is it?

• Linear function

• Quadratic function

• Exponential growth function

• Exponential decay function

When writing an exponential function from a graph, what does the 'a' value represent?

• Growth rate

• X-intercept

• Y-intercept

• Slope

If the y-intercept of a graph is 1 and the growth rate (b) is 3, what is the equation of the exponential function?

• y = 3^x

• y = 1 * 3^x

• y = 3 * x

• y = x^3

In a table, if the y-intercept is 12 and the common ratio is 1/4, what is the equation of the exponential function?

• y = 4 * (1/12)^x

• y = 12 * 4^x

• y = 12 * (1/4)^x

• y = 12 * (1/2)^x

What is the common ratio (b) if y1 is 6 and y2 is 30 in a table?

• 1/5

• 5

• 30

• 6

If Patricia's car depreciates at a rate of 33% each year, what is the decay rate (b) in the exponential function?

• 0.33

• 1.33

• 0.67

• 1.67

In a word problem, if an investment triples each year, what is the growth rate (b)?

• 1/3

• 2

• 3

• 1

If there were 20,000 cases of flu and it is expected to reduce to a third each month, what is the equation of the exponential function?

• y = 20000 * (1/3)^x

• y = 20000 * 3^x

• y = 20000 * (2/3)^x

• y = 20000 * (1/2)^x

If a vintage car's value increases at a rate of 33% each year, what is the growth rate (b) in the exponential function?

• 0.33

• 1.33

• 0.67

• 1.67