#### How to find the equation of an exponential function from a graph

## What is the formula for an exponential function?

Exponential functions have the form f(x) = b^{x}, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria.

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

If you have two points, (x_{1}, y_{1}) and (x_{2}, y_{2}), you can define the exponential function that passes through these points by substituting them in the equation y = ab^{x} and solving for a and b. In general, you have to solve this pair of equations: y_{1} = ab^{x1} and y_{2} = ab^{x2}^{,} .

## How do you find the equation of a graph?

To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept–this should be of the form (0, b). The y- coordinate is the value of b in the equation.

## What is an example of an exponential equation?

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by . To solve exponential equations with same base, use the property of equality of exponential functions . If b is a positive number other than 1 , then bx=by if and only if x=y .

## What is exponential form in math?

exponential form. • a way of representing repeated multiplications of the same number. by writing the number as a base with the number of repeats. written as a small number to its upper right.

## How do you find the equation of two points?

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

## How do you find the exponential function on a calculator?

On most graphing calculators your exponent key is the caret top key: ^. If you have the caret top key let’s practice taking 15 and raising it to the 5th power. To do this you would type in 15^5 and press your enter or = key.

## What is the formula of a function?

A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type. It is common to name a function either f(x) or g(x) instead of y. f(2) means that we should find the value of our function when x equals 2.

## How do you graph the equation of a line?

To graph a linear equation, we can use the slope and y-intercept.Locate the y-intercept on the graph and plot the point.From this point, use the slope to find a second point and plot it.Draw the line that connects the two points.

## How do you find the equation of a line?

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.