Fundamentals of Exponential Functions

Front

What is the y-intercept of an exponential function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, f(0)). For example, in the function y = a(b^x), the y-intercept is (0, a).

Front

How do you express an exponential growth function?

Back

An exponential growth function can be expressed in the form y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What is an exponential decay function?

Back

An exponential decay function is expressed as y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time period.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a(b^x), where 'a' is a constant, 'b' is the base (b > 0, b ≠ 1), and 'x' is the exponent.

Front

What does the base of an exponential function indicate?

Back

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

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that the graph of a function approaches but never touches. For exponential functions, the horizontal asymptote is often y = 0.

Front

How do you find the y-intercept of the function y = 15(1.35)^x?

Back

To find the y-intercept, substitute x = 0 into the function: y = 15(1.35)^0 = 15(1) = 15, so the y-intercept is (0, 15).

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the function is greater than 1, leading to an increase over time. Exponential decay occurs when the base is between 0 and 1, leading to a decrease over time.

Front

What is the y-intercept of the function y = 50(1.4)^x?

Back

The y-intercept is found by substituting x = 0: y = 50(1.4)^0 = 50(1) = 50, so the y-intercept is (0, 50).

Front

What type of function is f(x) = 2(1/7)^x?

Back

This function is an exponential decay function because the base (1/7) is less than 1.