Writing 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 of an exponential function represent in the context of growth or decay?

Back

The base of an exponential function indicates the growth or decay factor. If the base is greater than 1, it represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

How do you write an exponential decay function?

Back

An exponential decay function can be written in the form f(t) = a * (1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the decay rate in the context of exponential decay?

Back

The decay rate is the fraction of the quantity that decreases over a specific time period, often expressed as a percentage.

Tags

CCSS.HSF-IF.C.8B

Front

How can you determine the amount remaining after a certain time using an exponential function?

Back

You can determine the amount remaining by substituting the time value into the exponential function and calculating the result.

Front

What is the significance of the initial value in an exponential function?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What does the term 'half-life' refer to in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value in an exponential decay process.

Front

How do you convert a decay rate into a base for an exponential function?

Back

To convert a decay rate 'r' into a base, use the formula base = 1 - r.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(t) = a * (1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

Front

What is the difference between exponential growth and exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B