# GROWTH

Calculates predicted exponential growth by using existing data. GROWTH returns the y-values for a series of new x-values that you specify by using existing x-values and y-values. You can also use the GROWTH worksheet function to fit an exponential curve to existing x-values and y-values.

**Syntax**

**GROWTH**(**known_y's**,known_x's,new_x's,const)

**Known_y's** is the set of y-values you already know in the relationship y = b*m^x.

- If the array known_y's is in a single column, then each column of known_x's is interpreted as a separate variable.
- If the array known_y's is in a single row, then each row of known_x's is interpreted as a separate variable.
- If any of the numbers in known_y's is 0 or negative, GROWTH returns the #NUM! error value.

Known_x's is an optional set of x-values that you may already know in the relationship y = b*m^x.

- The array known_x's can include one or more sets of variables. If only one variable is used, known_y's and known_x's can be ranges of any shape, as long as they have equal dimensions. If more than one variable is used, known_y's must be a vector (that is, a range with a height of one row or a width of one column).
- If known_x's is omitted, it is assumed to be the array {1,2,3, ...} that is the same size as known_y's.

New_x's are new x-values for which you want GROWTH to return corresponding y-values.

- New_x's must include a column (or row) for each independent variable, just as known_x's does. So, if known_y's is in a single column, known_x's and new_x's must have the same number of columns. If known_y's is in a single row, known_x's and new_x's must have the same number of rows.
- If new_x's is omitted, it is assumed to be the same as known_x's.
- If both known_x's and new_x's are omitted, they are assumed to be the array {1,2,3, ...} that is the same size as known_y's.

Const is a logical value specifying whether to force the constant b to equal 1.

- If const is TRUE or omitted, b is calculated normally.
- If const is FALSE, b is set equal to 1 and the m-values are adjusted so that y = m^x.

**Remarks**

- Formulas that return arrays must be entered as array formulas after selecting the correct number of cells.
- When entering an array constant for an argument such as known_x's, use commas to separate values in the same row and semicolons to separate rows.

**Examples**

This example uses the same data as the LOGEST example. The sales for the 11th through the 16th months are 33,100, 47,300, 69,000, 102,000, 150,000, and 220,000 units, respectively. Assume that these values are entered into six cells named UnitsSold.

When entered as an array formula, the following formula predicts sales for months 17 and 18 based on sales for the previous six months:

`GROWTH(UnitsSold,{11;12;13;14;15;16},{17;18})`

equals {320,197;468,536}

If the exponential trend continues, sales for months 17 and 18 will be 320,197 and 468,536 units, respectively.

You could use other sequential numbers for the x-value arguments, and the predicted sales would be the same. For example, you could use the default value for known_x's, {1;2;3;4;5;6}:

`GROWTH(UnitsSold,,{7;8},)`

equals {320197;468536}