Review - Test 2

Front

What is the range of the exponential function?

Back

The range of an exponential function is all real numbers greater than 0, typically expressed as y > 0.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Which function represents an initial amount of $15 and an increase of 35% each year?

Back

The function is y = 15(1.35)^{x}.

Front

How do you write an exponential growth function for a value that increases by a certain percentage?

Back

The function is written as y = initial value * (1 + growth rate)^{x}.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^{t}, where a is the initial amount, r is the growth rate, and t is time.

Front

What does the variable 'x' represent in an exponential function?

Back

In an exponential function, 'x' typically represents time or the number of periods.

Front

What is the significance of the base in an exponential function?

Back

The base of an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you determine the domain of an exponential function from a graph?

Back

The domain can be determined by identifying the x-values for which the function is graphed; for example, if the graph starts at x = -2, the domain is x > -2.

Front

What is the initial value in an exponential growth function?

Back

The initial value is the starting amount before any growth occurs, often represented as 'a' in the function y = a(1 + r)^{t}.

Front

How do you express a 9% increase in value in an exponential function?

Back

A 9% increase can be expressed as y = initial value * (1.09)^{x}.