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 a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify an exponential growth graph?

Back

An exponential growth graph rises steeply as x increases, showing a J-shaped curve.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify an exponential decay graph?

Back

An exponential decay graph falls steeply as x increases, approaching the x-axis but never touching it.

Tags

CCSS.HSF-IF.C.7E

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the initial value of the function, found by evaluating f(0). For f(x) = a(b^x), it is 'a'.

Tags

CCSS.HSF-IF.C.7E

Front

If a function has a base greater than 1, what type of function is it?

Back

It is an exponential growth function.

Front

If a function has a base between 0 and 1, what type of function is it?

Back

It is an exponential decay function.

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'initial value' refer to in an exponential function?

Back

The initial value is the starting amount of the quantity before any growth or decay occurs, represented by 'a' in f(x) = a(b^x).

Tags

CCSS.HSF-IF.C.8B