Writing Exponential Equations

Front

What is an Exponential Function?

Back

A function where the variable is in the exponent, typically in the form f(x) = a(b)^x, where a is a constant and b is the base.

Front

What is Exponential Growth?

Back

A situation where a quantity increases by a consistent percentage over time, represented by an exponential function with a base greater than 1.

Front

What is Exponential Decay?

Back

A situation where a quantity decreases by a consistent percentage over time, represented by an exponential function with a base between 0 and 1.

Front

What is a Linear Function?

Back

A function that creates a straight line when graphed, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a Common Ratio?

Back

The factor by which a quantity is multiplied in each step of an exponential function, found by dividing any term by the previous term.

Front

Identify the common ratio in f(x)=2(4)^x.

Back

4, because each time x increases by 1, f(x) is multiplied by 4.

Front

If f(x) values are divided by 3, what is the common ratio?

Back

1/3, indicating that each term is multiplied by 1/3.

Front

What does the equation f(x)=2(1/7)^x represent?

Back

Exponential Decay, because the base (1/7) is less than 1.

Front

What is the difference between Exponential Growth and Exponential Decay?

Back

Exponential Growth increases over time, while Exponential Decay decreases over time.

Front

How can you identify an Exponential Function from a table?

Back

Look for a pattern where each output value is multiplied by a constant factor as the input increases.