Exponential Functions Review

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 a positive real number, and 'x' is the exponent.

Front

What is the difference between exponential growth and decay?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the decay factor in an exponential decay model?

Back

The decay factor is the value by which the quantity decreases in each time period, calculated as 1 - decay rate.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify an exponential decay function from a formula?

Back

An exponential decay function can be identified by a formula of the form A = A0 * (1 - r)^t, where A0 is the initial amount, r is the decay rate, and t is time.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is a_n = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio 'r' can be found by dividing any term by the previous term in the sequence.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is A = A0 * (1 + r)^t, where A0 is the initial amount, r is the growth rate, and t is time.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for a function to be exponential?

Back

A function is considered exponential if it can be expressed in the form f(x) = a * b^x, where 'b' is a constant greater than 0.

Front

How do you write an explicit formula for a sequence given its terms?

Back

To write an explicit formula for a sequence, identify the pattern in the terms and express it in the form a_n = a * r^(n-1) or similar.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The base in an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B