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(b^0) = a.

Front

How do you simplify the expression (3x^4)(5x^3)?

Back

To simplify, multiply the coefficients and add the exponents: (3*5)x^(4+3) = 15x^7.

Front

What is the common ratio in an exponential function?

Back

The common ratio in an exponential function is the factor by which the function's value changes as x increases by 1, represented as b in f(x) = a(b^x).

Front

How do you find the common ratio from a table of values?

Back

To find the common ratio, divide any f(x) value by the previous f(x) value in the table.

Front

What is the simplified form of 10x^-2?

Back

The simplified form is 10/(x^2) or 10x^2 when expressed with positive exponents.

Front

What does it mean for a function to be exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a(b^x), where the variable x is in the exponent.

Front

How do you identify the base of an exponential function?

Back

The base of an exponential function is the number that is raised to the power of x, represented as 'b' in f(x) = a(b^x).

Front

What is the general form of an exponential growth function?

Back

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