Exponential Growth and Decay review

What does the base 'b' represent in an exponential function?

• 'b' represents the growth or decay factor.

• 'b' represents the rate of change in a linear function.

• 'b' is the y-intercept of the function.

• 'b' indicates the maximum value of the function.

How can you determine if a table of values represents exponential growth or decay?

• Find the quotients (divide) each pair of consecutive outputs. If the values are constant, it indicates exponential growth or decay. If they are increasing, it's growth; if decreasing, it's decay.

• Calculate the average of all outputs. If the average is increasing, it's growth; if decreasing, it's decay.

• Look for the maximum and minimum values in the table. If the maximum is increasing, it's growth; if decreasing, it's decay.

• Check if the outputs are all positive numbers. If they are, it indicates growth; if any are negative, it's decay.

What is exponential growth? Define & give an example

• A constant increase by a factor (multiplier) that is greater than 1

• A linear increase over time

• A decrease in population size

• A random fluctuation in population numbers

What is exponential decay? Define & give an example

• A constant increase by a factor (multiplier) that is between 0 and 1.

• A constant decrease by a factor (multiplier) that is greater than 1.

• A random fluctuation in value over time.

• A steady increase in value over time.

What is the difference between exponential growth and decay in terms of their equations?

• Exponential growth has a base between 0 and 1 (0 < b < 1), while exponential decay has a positive base (b > 1).

• Exponential growth has a positive base (b > 1), while exponential decay has a base between 0 and 1 (0 < b < 1).

• Exponential growth and decay both have a base of 1.

• Exponential growth has a negative base (b < 0), while exponential decay has a base of 1.

How can you tell if a graph shows exponential growth?

• The graph is a straight line from left to right.

• The graph curves upward from the y-intercept at a faster and faster rate from left to right.

• The graph shows a constant increase at a steady rate.

• The graph fluctuates up and down without a clear trend.

What is a common real-world example of exponential growth?

• A common example is compound interest in finance, where the amount of interest earned grows exponentially over time.

• The population of a city increasing by a fixed number each year.

• The growth of a tree in height over a decade.

• The decrease in the number of fish in a pond due to overfishing.

What is the real-world meaning of the y-intercept in an exponential function?

• It represents the starting point or initial value of the function.

• It indicates the maximum value the function can reach.

• It shows the rate of growth of the function.

• It represents the average value of the function over time.

Is y = 5000(3/5)^x an example of exponential growth or decay?

• Exponential growth as 'b' is greater than 1

• Exponential decay as 'b' or 3/5 is between 0 and 1

• Linear growth

• Constant growth

Is y = 200(7/5)^x an example of exponential growth or decay?

• Exponential growth as 'b' or 7/5 is less than 1

• Exponential decay as 'b' or 7/5 is greater than 1

• Linear growth as 'b' or 7/5 equals 1

• Constant function as 'b' or 7/5 is equal to 0