Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Tags

CCSS.HSF-LE.A.1A

Front

What is the common ratio in an exponential sequence?

Back

The common ratio in an exponential sequence is the factor by which each term is multiplied to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

How can you identify exponential growth from its function?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1 (b > 1).

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify exponential decay from its function?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a * b^x is between 0 and 1 (0 < b < 1).

Tags

CCSS.HSF-IF.C.8B

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly at first and then levels off, approaching the x-axis but never touching it.

Tags

CCSS.HSF-IF.C.7E

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a larger base results in faster growth, while a base between 0 and 1 results in decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the effect of a negative exponent in an exponential function?

Back

A negative exponent indicates a reciprocal; for example, b^(-x) = 1/(b^x), which can represent decay.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What is a real-world example of exponential decay?

Back

A real-world example of exponential decay is radioactive decay, where the quantity of a radioactive substance decreases over time.