Exponential Functions

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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.

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

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, resulting in a rapid increase over time.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to a rapid decrease over time.

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify an exponential function from its equation?

Back

An exponential function can be identified by the variable being in the exponent, such as in f(x) = a * b^x.

Front

What is the base in an exponential function?

Back

The base in an exponential function is the constant 'b' that determines the rate of growth or decay.

Tags

CCSS.HSF-IF.C.8B

Front

What does the initial value represent in an exponential function?

Back

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

Tags

CCSS.HSF.LE.B.5

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What does the expression 12(1.015)^t represent in terms of population?

Back

It represents the population of elephants in a wildlife refuge, where 12 is the initial population and 1.015 is the growth factor.

Tags

CCSS.HSF-IF.C.8B

Front

How can you tell if a graph represents exponential growth or decay?

Back

If the graph rises steeply as it moves to the right, it represents exponential growth; if it falls steeply, it represents exponential decay.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^(-x), where 'b' is greater than 1.