Exponential Growth vs Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. Example: y = a(1 + r)^t, where 'r' is the growth rate.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: y = a(1 - r)^t, where 'r' is the decay rate.

Front

Identify the equation for exponential growth: y = 3(5)^x, y = 0.5(5)^x, y = 2(0.5)^x, y = 8(1)^x

Back

y = 3(5)^x

Front

Identify the equation for exponential decay: y = 3(5)^x, y = 0.5(5)^x, y = 2(0.5)^x, y = 8(1)^x

Back

y = 2(0.5)^x

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay factor. If the base is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

Front

What is the general form of an exponential function?

Back

The general form is y = a(b)^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent.

Front

How does the value of 'a' affect the graph of an exponential function?

Back

The value of 'a' affects the vertical stretch or compression of the graph. A larger 'a' results in a higher graph, while a smaller 'a' results in a lower graph.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster growth over time.

Front

What is a real-world example of exponential growth?

Back

Population growth in a species under ideal conditions is a common example of exponential growth.

Front

What is a real-world example of exponential decay?

Back

Radioactive decay of a substance is a common example of exponential decay.