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 base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

What is the initial value in an exponential function?

Back

The initial value is the value of the function when x = 0, represented by 'a' in the function f(x) = a * b^x.

Front

Solve: 2^(x+1) = 512

Back

x = 8

Front

What is the formula for finding the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

Identify the common ratio in the geometric sequence: 3, 9, 27, ...

Back

The common ratio is 3.

Front

What is the 14th term of the geometric sequence: 3, 9, 27, ...?

Back

The 14th term is 4,782,969.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.

Front

Find the 11th term for the sequence: 64, -32, 16, -8, ...

Back

The 11th term is -0.0625.

Front

True or False: 3, 15, 75, ... is an arithmetic sequence.

Back

False.