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.

Front

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.

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.

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.

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.

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.

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.

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.