IA Exponential Growth Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It can be represented by the equation y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is exponential decay?

Back

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time. It can be represented by the equation y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

Identify the general form of an exponential function.

Back

The general form of an exponential function is y = a(b)^x, where 'a' is a constant (initial value), 'b' is the base (growth or decay factor), and 'x' is the exponent.

Front

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

Back

In an exponential function y = a(b)^x, the base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor. It determines how quickly the function increases or decreases.

Front

What is the y-intercept in an exponential function?

Back

The y-intercept of an exponential function y = a(b)^x is the value of 'y' when 'x' = 0, which is equal to 'a'.

Front

How do you determine if a function represents exponential growth or decay?

Back

If the base 'b' in the function y = a(b)^x is greater than 1, it represents exponential growth. If 'b' is between 0 and 1, it represents exponential decay.

Front

What is the decay factor in the function y = 205(0.25)^x?

Back

The decay factor in the function y = 205(0.25)^x is 0.25, indicating that the value decreases to 25% of its previous amount for each unit increase in 'x'.

Front

Which of the following is an example of exponential decay: y = 3(5)^x or y = 2(0.5)^x?

Back

y = 2(0.5)^x is an example of exponential decay because the base (0.5) is less than 1.

Front

What is the initial value in the function y = 15(1.35)^x?

Back

The initial value in the function y = 15(1.35)^x is 15, which is the value of 'y' when 'x' = 0.

Front

What does it mean if a function has a base of 0.35?

Back

If a function has a base of 0.35, it indicates exponential decay, as the value decreases over time.