Exponential Functions

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 a positive real number, and 'x' is the exponent.

Front

What distinguishes exponential growth from exponential decay?

Back

Exponential growth occurs when the base 'b' in the function y = a(b^x) is greater than 1, while exponential decay occurs when 'b' is between 0 and 1.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a(b^x) is the point where x = 0, which is (0, a).

Front

How do you identify if a function is linear or exponential?

Back

A function is linear if it can be expressed in the form y = mx + b, where m and b are constants. An exponential function has a variable in the exponent.

Front

What is the general form of an exponential growth equation?

Back

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

Front

What is the general form of an exponential decay equation?

Back

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

Front

Given the function y = 3(2^x), is it exponential growth or decay?

Back

Exponential growth, because the base 2 is greater than 1.

Front

Given the function y = 5(0.5^x), is it exponential growth or decay?

Back

Exponential decay, because the base 0.5 is less than 1.

Front

What is the y-intercept of the function y = 4(3^x)?

Back

The y-intercept is (0, 4), since when x = 0, y = 4(3^0) = 4.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept, substitute x = 0 into the function and solve for y.