Exponential Graphs: Understanding Growth and Decay

The video tutorial explains exponential growth and decay, using examples like money doubling and tennis tournaments. It covers the properties of exponential graphs, including how they curve upwards for growth and downwards for decay. The tutorial also discusses the mathematical representation of these graphs and how to calculate values using powers.

What does exponential growth mean in terms of the Y-axis as the X-axis increases?

• The Y-axis value remains constant.

• The Y-axis value decreases at a slower rate.

• The Y-axis value rises at a faster rate.

• The Y-axis value decreases at a faster rate.

Which of the following is an example of exponential decay?

• Bacteria doubling every half hour

• Radioactive half-life

• Compound interest

• Population growth

In the money-doubling example, what mathematical concept is used to represent the growth?

• Powers of ten

• Powers of three

• Powers of five

• Powers of two

If you start with £1 and double it every day, how much will you have after 10 days?

• £512

• £256

• £1024

• £2048

What is the significance of the Y-intercept in an exponential growth graph?

• It is always two.

• It is always negative.

• It is always one.

• It is always zero.

What happens to the Y-axis value as the power of X becomes negative in an exponential graph?

• It becomes a fraction.

• It becomes an integer.

• It becomes zero.

• It becomes negative.

In the tennis tournament example, how is the reduction of competitors represented mathematically?

• Adding 2

• Multiplying by 1/2

• Dividing by 2

• Multiplying by 2

What is the form of the equation for exponential decay?

• Y = K^X

• Y = K^-X

• Y = X^K

• Y = -K^X

How can you find the value of K in an exponential equation?

• By finding the value of X when Y = 1

• By finding the value of X when Y = 0

• By finding the value of Y when X = 1

• By finding the value of Y when X = 0

What does the graph of Y = K^-X represent?

• Exponential decay

• Linear growth

• Exponential growth

• Linear decay