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Equation for an Exponential Growth Curve

The Excel Growth Function finds the exponential trend by calculating the curve of best fit for the equation

- x is the independent variable

- y is the dependent variable

- b is a constant which is the value of y when x = 0

- m is the growth factor

This is explained in more detail on the Wikipedia Exponential Growth PageThe Excel GROWTH function calculates the exponential growth curve through a given set of y-values and (optionally), a given set of x-values. The function then extends the curve to calculate additional y-values for a further supplied set of new x-values.

The format of the function is :

GROWTH( known_y's, [known_x's], [new_x's], [const] )

Where the arguments are described in the table below :

known_y's | - | A set of known y-values |

[known_x's] | - | A set of known x-values. This is an optional argument which, if provided, should have the same length as the set of known_y's If omitted, the set of [known_x's] takes on the value {1, 2, 3, ...} |

[new_x's] | - | A set of new x-values, for which the function calculates corresponding new y-values If omitted, the set of [new_x's] is assumed to be the same as the [known_x's] and the function calculates the y-values that lie on calculated exponential growth curve |

[const] | - | An optional logical argument that specifes whether the constant 'b', in the equation If [const] is TRUE (or if this argument is omitted) the constant b is treated normally; If [const] is FALSE the constant b is set to 1 and the equation becomes |

As the Growth function returns an array of values, it must be entered as an Array Formula.

Array Formulas:

To input an array formula, you need to first highlight the range of cells for the function result. Type your function into the first cell of the range, and press CTRL-SHIFT-Enter.Go to the Excel Array Formulas page for more details.

The spreadsheet below shows a simple example of the Excel Growth Function being used to extend a series of x- and y-values that lie on the exponential growth curve y = 5 * 2^x. These are stored in cells A2 - B5 of the spreadsheet and are also shown in the graph.

The Growth function calculates the exponential growth curve that has the best fit for the provided known x- and y- values. In this simple example, the curve of best fit is the exponential curve y = 5 * 2^x.

Once Excel has calculated the exponential growth curve equation, it can use this to calculate the new y-values for the provided new x values in cells A8 - A10.

In this example, the values of the [new_x's] are stored in cells A8 - A10 and the Excel Growth function has been entered into cells B8 - B10, to find the corresponding new y values. The equation for this, as shown in the formula bar, is :

=GROWTH( B2:B5, A2:A5, A8:A10 )

It is seen that the Growth function in the formula bar is encased in curly braces { }. This indicates that the function has been input as an Array Formula.

Note that, although the points in the example fit exactly along the curve y = 5 * 2^x, this is not essential. The Excel Growth function will find the curve of best fit for any set of values provided to it.

Further examples of the Excel Growth function can be found on the Microsoft Office website.

The most common errors from the Excel Growth function are listed in the table below :

Common Errors

#REF! | - | Occurs if the [known_x's] array has a different length to the known_y's array. |

#NUM! | - | Occurs if any of the values in the known_y's array are less than or equal to 0. |

#VALUE! | - | Occurs if any of the values in the supplied known_y's, [known_x's] or [new_x's] arrays are non-numeric. |