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 it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals, represented by a function where the base 'b' is greater than 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over equal time intervals, represented by a function where the base 'b' is between 0 and 1.

Front

Identify the base in the exponential function A = 10(1.01)^3.

Back

The base is 1.01.

Front

In the function y = 15(1.35)^x, what does the '15' represent?

Back

The '15' represents the initial amount or starting value before any growth occurs.

Front

How can you determine if an exponential function represents growth or decay?

Back

If the base 'b' is greater than 1, it represents growth; if 'b' is between 0 and 1, it represents decay.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b^x) where 'a' > 0 and 'b' > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x) where 'a' > 0 and 0 < 'b' < 1.

Front

If a population of rabbits is decreasing, what type of function would represent this situation?

Back

An exponential decay function.

Front

What is the significance of the exponent in an exponential function?

Back

The exponent indicates the number of time intervals that have passed, affecting the growth or decay of the quantity.