Exponential and Logarithmic Graphs

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where a > 0 and 0 < b < 1.

Front

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation a^b = c to logarithmic form, use the formula log_a(c) = b.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = a^x, then x = log_a(y).

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.718.

Front

How do you express log_a(b) in terms of natural logarithms?

Back

log_a(b) can be expressed as ln(b) / ln(a) using the change of base formula.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises rapidly as x increases, starting from a positive y-intercept.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching the x-axis but never touching it.

Front

What is the effect of a vertical translation on the graph of an exponential function?

Back

A vertical translation shifts the graph up or down without changing its shape.

Front

How do you find the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept because it never touches the x-axis.