Writing Exponential Equations from Initial Values and Rates

The video tutorial explains how to write exponential equations based on given information. It covers the forms of exponential growth and decay equations, where the base is adjusted by a growth or decay rate. Examples are provided for both growth and decay scenarios, illustrating how to convert percentage rates into decimals and apply them to the equations. The tutorial concludes with simplified forms of the equations.

What is the general form of an exponential growth equation?

• y = a * (1 + r)^x

• y = a * (1 - r)^x

• y = a / (1 - r)^x

• y = a / (1 + r)^x

What does the variable 'r' represent in the exponential equation?

• Base of the equation

• Growth or decay rate as a decimal

• Initial value

• Final value after one period

If the initial value is 441 and the growth rate is 26%, what is the value of 'a' in the exponential equation?

• 0.26

• 441

• 467

• 26

Convert a 9% growth rate into decimal form.

• 0.09

• 9

• 0.009

• 0.9

If the initial value is 215 and the growth rate is 9%, what is the base of the equation?

• 215

• 0.09

• 1.9

• 1.09

For an initial value of 92 and a decay rate of 3%, what does 'a' represent in the equation?

• 92

• 95

• 0.03

• 3

What is the base of the exponential equation for a decay rate of 3%?

• 0.03

• 1.03

• 1.03

• 0.97

How is the decay rate of 50% expressed as a decimal?

• 5

• 0.5

• 50

• 0.50

What is the simplified form of the exponential decay equation if the decay rate is 50%?

• y = 444 * 0.5^x

• y = 444 * (1 + 0.5)^x

• y = 444 * 1.5^x

• y = 444 * (1 - 0.5)^x

What is the correct equation for an initial value of 444 and a decay rate of 50%?

• y = 444 * (1 - 0.5)^x

• y = 444 * (1 + 0.5)^x

• y = 444 * 0.5^x

• y = 444 * 1.5^x