Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What is the formula for exponential growth?

Back

The formula is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

What is the formula for exponential decay?

Back

The formula is f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

What does the variable 'b' represent in the function f(x) = a(b)^x?

Back

In this function, 'b' is the base or common ratio that determines the growth or decay factor.

Front

How do you identify exponential growth from a table of values?

Back

Exponential growth can be identified if the ratio of consecutive values remains constant.

Front

How do you identify exponential decay from a table of values?

Back

Exponential decay can be identified if the ratio of consecutive values remains constant and is less than 1.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300, which is the value of f(0).

Front

What is the common ratio in the function f(x) = 300(1.16)^x?

Back

The common ratio is 1.16, indicating a growth factor of 16%.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change.