9.2 Work - Writing Exponential Functions from a Graph

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 the base (a positive real number), and 'x' is the exponent.

Front

What does the Y-intercept represent in an exponential function?

Back

The Y-intercept is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a * b^x.

Front

How do you identify the base of an exponential function from a graph?

Back

The base 'b' can be identified by observing the growth rate of the function; it is the factor by which the function value increases for each unit increase in x.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth (b > 1) or decay (0 < b < 1) factor.

Front

How do you write an exponential function from a graph?

Back

To write an exponential function from a graph, identify the Y-intercept (value of f(0)) and the growth/decay factor (base) by analyzing the rate of change.

Front

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

Back

The base determines the rate of growth or decay; if b > 1, the function grows exponentially, and if 0 < b < 1, the function decays exponentially.

Front

How can you determine if a function is exponential from a table of values?

Back

A function is exponential if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are equally spaced.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, while exponential decay occurs when the base 'b' is between 0 and 1.

Front

How do you find the equation of an exponential function given two points?

Back

Use the two points to set up a system of equations based on the form f(x) = a * b^x, then solve for 'a' and 'b'.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'k' is the growth rate, and 't' is time.