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 y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is f(0) = a.

Front

How do you find the y-intercept of the function y = 2^x?

Back

To find the y-intercept, substitute x = 0: y = 2^0 = 1.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which each term of a geometric sequence is multiplied to get the next term.

Front

If the first term of a geometric sequence is 28 and the second term is 14, what is the common ratio?

Back

The common ratio is 14/28 = 1/2.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, for any two points x1 and x2 where x1 < x2, f(x1) < f(x2).

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 difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base b > 1, while exponential decay occurs when the base 0 < b < 1.

Front

How do you simplify the expression 10x^-2?

Back

10x^-2 can be simplified to 10/(x^2).

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a * b^x, where a is a non-zero constant and b is a positive real number.