The GROWTH function 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.

### Syntax

=GROWTH(known_y’s,[known_x’s],[new_x’s],[const])

#### Arguments

Argument Description
known_y’s 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
[known_x’s] Optional. An optional set of x-values that you may already know in the relationship y = b*m^x

 • If provided, the [known_x’s] 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, …} that is the same size as known_y’s
[new_x’s] Optional. Are new x-values for which you want GROWTH to return corresponding y-values

 • If omitted, the set of [new_x’s] is assumed to be the same as the [known_x’s] and the function returns the y-values that lie on calculated exponential growth curve • 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] Optional. A logical value specifying whether to force the constant b to equal 1

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

Note: If more than one new y-value is to be calculated by the GROWTH function, the new values will be returned as an array. Therefore, the function must be entered as an array formula.

• 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

A B C D E
1 Month (Xs) Sales (Ys) Corresponding Units    nowrap
2 2 330 338.39
3 3 480 472.20
4 4 650 658.92
5 5 1,000 919.47
6 6 1,200 1,283.06 Array formula used in C2:C7
7 7 1,800 1,790.41 {=GROWTH(B2:B7,A2:A7)}
8
9 New Xs New Ys   Array formula used in B10:B11
10 8 2,498.37   {=GROWTH(B2:B7,A2:A7,A10:A11)}
11 9 3,486.28

Note: The curly brackets, { and }, seen in the formula entered in D7 and D10 are not entered by the user. Excel applies these to show the formula has been input as an array formula.

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the values in the supplied known_y’s[known_x’s] or [new_x’s] arrays are non-numeric
#NUM! Occurs if any of the values in the known_y’s array are less than or equal to 0
#REF! Occurs if the [known_x’s] array has a different length to the known_y’s array

For a single range of x-values, the equation for an exponential curve is:  where,

• x is the independent variable
• y is the dependent variable
• m is a constant base for the x value
• b is a constant which is the value of y when x = 0

If there are multiple ranges of x-values, the exponential curve equation is: