GROWTH

Fits an exponential curve to a data set, and returns points on that curve.

Syntax:

GROWTH(yvalues, xvalues, new_xvalues, allow_factor)

data is a range or array containing numerical data.

yvalues and xvalues are single row or column ranges specifying points in a set of data.

GROWTH fits an exponential curve of the form y=bmx through these data points, using the linear regression method.

If allow_factor is FALSE the factor b in this equation is set to 1; if allow_factor is non-zero, TRUE or omitted the factor b is calculated from the data.

GROWTH returns an array of the y values of the exponential curve found, corresponding to the x values in new_xvalues (or if omitted xvalues). It must be entered as an array formula.

yvalues and xvalues must be the same size. new_xvalues may have a different size.

Example:

GROWTH(B2:B6, A2:A6, A2:A7)

when entered as an array formula in cell C2, where the x values in A2:A7 are 4, 5, 6, 7, 8, 9 and the y values in B2:B6 are 1.80, 3.20, 6.20, 12.30, 24.50, finds a best fit exponential curve for those points, and in C2:C7 returns y values on that curve for the x values in A2:A7.This example shows how GROWTH may be used to predict future values (A7,C7).

Application:

Scenario: A small e-commerce business, "Gadget Guru," has been tracking its quarterly revenue for the past two years. The owner wants to forecast the revenue for the next three quarters to plan for hiring and inventory. They believe the business is experiencing exponential growth due to their effective marketing strategy.

Known Data (Historical Revenue):

The owner has the following data for the past eight quarters:

	Quarter	Period (X-values)	Revenue (Y-values)
	A	B	C
1	Q1 2023	1	$15,000.00
2	Q2 2023	2	$16,500.00
3	Q3 2023	3	$18,150.00
4	Q4 2023	4	$19,965.00
5	Q1 2024	5	$21,962.00
6	Q2 2024	6	$24,158.00
7	Q3 2024	7	$26,574.00
8	Q4 2024	8	$29,231.00

Goal: Forecast the revenue for the next three quarters (Q1 2025, Q2 2025, and Q3 2025).

Applying the GROWTH function:

The GROWTH function has the following syntax:

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

known_y's: The range of the historical revenue data (e.g., C1:C8).
known_x's: The range of the corresponding periods (e.g., B1:B8).
new_x's: The range of the periods for which you want to forecast (e.g., B9:B10, which would contain the values 9, 10, and 11).
const: A logical value. If TRUE or omitted, the constant 'b' is calculated normally. If FALSE, the constant 'b' is set to 1. For this example, we'll omit it as we want the function to calculate the best-fit exponential curve.

Spreadsheet Implementation:

Let's assume the data above is in a spreadsheet.

Known_y's: C1:C8
Known_x's: B1:B8
New_x's: B9:B11 (where B9 has 9, B10 has 10, and B11 has 11)

To get the forecasted values, you would use an array formula.

GROWTH(C1:C8, B1:B8, B9:B11)

Forecasted Table (Results):

The function would return the following predicted values, which you can format to two decimal places:

	Quarter	Period (New X-values)	Forecasted Revenue (New Y-values)
	A	B	C
1	Q1 2025	9	$32,154.10
2	Q2 2025	10	$35,370.47
3	Q3 2025	11	$38,907.51

Explanation:

The GROWTH function works by fitting an exponential curve to the historical data. It determines the underlying growth rate and starting value that best explain the past trend. It then uses this calculated formula to project the values for the new periods. This is a powerful tool for forecasting because it assumes that the underlying growth pattern observed in the past will continue into the future, which is a common and reasonable assumption for many business metrics.