Understanding Exponential Equations

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. The tutorial provides examples of both growth and decay, detailing how to convert percentage rates into decimals and apply them to the equations. The lesson concludes with simplified forms of the equations, emphasizing the importance of understanding initial values and rates.

What is the general form of an exponential equation?

• y = a + bx

• y = a * b^x

• y = a / b^x

• y = a - bx

In exponential growth, how is the base 'b' calculated?

• b = 1 + r

• b = r + 1

• b = 1 - r

• b = r - 1

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

• y = 441 * 1.26^x

• y = 441 * 0.74x

• y = 441 * 0.74^x

• y = 441 * 1.26x

How do you express a 9% growth rate as a decimal?

• 0.009

• 9.0

• 0.9

• 0.09

What is the exponential equation for an initial value of 215 and a growth rate of 9%?

• y = 215 * 1.09x

• y = 215 * 0.91x

• y = 215 * 0.91^x

• y = 215 * 1.09^x

In exponential decay, how is the base 'b' calculated?

• b = r - 1

• b = 1 + r

• b = 1 - r

• b = r + 1

If the initial value is 92 and the decay rate is 3%, what is the exponential equation?

• y = 92 * 0.97^x

• y = 92 * 1.03^x

• y = 92 * 0.97x

• y = 92 * 1.03x

How do you express a 50% decay rate as a decimal?

• 5.0

• 0.5

• 50.0

• 0.05

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

• y = 444 * 0.5x

• y = 444 * 1.5x

• y = 444 * 1.5^x

• y = 444 * 0.5^x

What does the 'a' represent in the exponential equation y = a * b^x?

• The growth rate

• The decay rate

• The initial value

• The exponent