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: y = bm^x  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:    

    \[    y = (b)(m_1^{x_1})(m_2^{x_2}) \cdots (m_n^{x_n})    \]