Pre-Calculus P1 HW 01.06.25: graphs of Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = 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 at a rate proportional to its current value, typically represented by a function of the form y = a(b^x) where b > 1.

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, typically represented by a function of the form y = a(b^x) where 0 < b < 1.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth graphs rise steeply as x increases, showing a rapid increase in y values.

Front

How can you identify exponential decay from a graph?

Back

Exponential decay graphs fall steeply as x increases, showing a rapid decrease in y values.

Front

What is the general form of an exponential growth equation?

Back

The general form is y = a(b^x) where b > 1.

Front

What is the general form of an exponential decay equation?

Back

The general form is y = a(b^x) where 0 < b < 1.

Front

What effect does changing the base 'b' have on the graph of an exponential function?

Back

Changing the base 'b' affects the rate of growth or decay; larger bases lead to faster growth, while bases between 0 and 1 lead to faster decay.

Front

What does the 'a' value represent in an exponential function?

Back

The 'a' value represents the initial value or the y-intercept of the function.

Front

What is the y-intercept of the function y = 2^(x+3)?

Back

The y-intercept occurs when x = 0, so y = 2^(0+3) = 2^3 = 8.