Exponential Growth and Decay Concepts

This video tutorial introduces exponential equations, explaining their structure and components, such as initial value and base. It covers exponential growth and decay, illustrating how graphs change based on the base value. The tutorial provides formulas for calculating growth and decay rates and demonstrates these concepts through examples. Finally, it guides viewers on constructing exponential equations from given data, emphasizing the importance of converting rates to decimals.

What is the initial value in an exponential equation?

• The value of x when y is zero

• The exponent in the equation

• The y-value when x is zero

• The base of the equation

If the base of an exponential equation is greater than one, what does the graph represent?

• Constant function

• Exponential growth

• Linear growth

• Exponential decay

What happens to the graph of an exponential equation if the base is between zero and one?

• It remains constant

• It shows exponential growth

• It shows exponential decay

• It becomes a linear graph

In the equation y = 12 * 1.2^x, what is the growth rate as a percentage?

• 10%

• 20%

• 15%

• 25%

For the equation y = 5 * 0.85^x, what is the decay rate as a percentage?

• 10%

• 25%

• 20%

• 15%

How do you express a growth rate of 6.2% as a decimal?

• 0.062

• 0.62

• 6.2

• 0.0062

What is the equation form for exponential decay?

• y = a * (1 + r)^x

• y = a * (1 - r)^x

• y = a * b^x

• y = a * x^b

If the initial value is 81 and the decay rate is 12.5%, what is the base of the equation?

• 0.875

• 0.8125

• 1.125

• 0.125

What is the base b in the equation y = 9.2 * 1.062^x?

• 1.062

• 0.062

• 9.2

• 1.2

What is the decay rate if the base b is 0.875?

• 10%

• 15%

• 8.75%

• 12.5%