Exponential Functions and Sequences

Front

What is an exponential function?

Back

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

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal time intervals, resulting in a rapid decrease.

Front

How do you identify an exponential function from a table of values?

Back

An exponential function can be identified if the ratio of consecutive outputs (y-values) remains constant when the inputs (x-values) are increased by equal intervals.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a(b)^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

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

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

If a car's value increases by 10% each year, how do you calculate its value after several years?

Back

To calculate the future value, use the formula: Future Value = Present Value * (1 + rate)^number of years.

Front

What is the value of 3^4?

Back

3^4 = 81.