In Unit 5, you dealt solely with polynomial functions such as f(x) = x3 that have a constant exponent and variable base. This lesson considers functions such as g(x) = 5x, which have a variable exponent and a constant base. Known as exponential functions, these functions are important because of the wide variety of their applications. Lesson 6C introduces several of these applications including compound interest, radioactive decay, and population growth.

Determine whether each equation represents an exponential function.
  1. This is not an exponential function. The exponent is a number, 3, but for an exponential function, the exponent must be a variable. The base is a variable. For an exponential function, the base should be a positive number.

  1. This is an exponential function. The leading coefficient is , the base is 5, which is a positive real number, and the exponent is the variable x.

  1. This is an exponential function. The leading coefficient is 1, the base is 0.3, which is a positive real number, and the exponent is the variable x.

  1. This is not an exponential function because the base, -4, is not a positive real number.