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 does the base 'b' in an exponential function represent?

Back

The base 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

What is the common ratio in the function f(x)=2(4)^x?

Back

The common ratio is 4.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100.

Front

What is 5% as a decimal?

Back

0.05

Front

What does the 'a' represent in the exponential function f(x) = a(b)^x?

Back

The 'a' represents the y-intercept of the function.

Front

What is the y-intercept of the function y = 50(1.4)^x?

Back

The y-intercept is 50.

Front

What is an increasing exponential function?

Back

An increasing exponential function is one where the base 'b' is greater than 1, resulting in the function rising as 'x' increases.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x, where 'r' is the growth rate.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(1 - r)^x, where 'r' is the decay rate.