# GROWTH Function

#### Basic Description

The 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.

**Syntax:** 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 y = b * m^x, should be forced to be equal to the value 1.
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.

#### Growth Function Example

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 :

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.

#### Growth Function Errors

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

#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. |