I would suggest:
=INT(FORECAST(E22, $C$5:$C$21, $E$5:$E$21))
formatted as a date, where E22 contains the minimum amount (zero?).
But I would do my "homework" first (pun intended).
That would explain, for instance, why I would start with C5 and E5, excluding the first 3 data points.
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For the same "known Y" (column C) and "known X" (column E) data, FORECAST and LINEST use the same linear formula to estimate the best-fit straight line, namely y = x*m + b.
(Also, SLOPE returns m, and INTERCEPT returns b.)
We cannot use LINEST directly to extrapolate the data. But we might use the values returned by LINEST (or SLOPE and INTERCEPT) in a formula of the form =x*m + b, substituting appropriate cell references.
FORECAST is a simpler way to calculate the same result.
But in all cases, we assume that a straight-line fits the original data well, if not "the best".
We should confirm that assumption by
charting the data first to determine which trendline fits the data best.
To that end, it would be prudent to use
relative day numbers instead of actual dates, with 1 corresponding to the first date (10/10/2020). Thus, starting with B3, we might enter formulas of the form
=C3-C2+B2 into column B.
The reason is: Excel dates are represented by integers, which are 5 digits these nowadays. For example, today (Feb 13 2021) is represented by 44240. Some trendlines raise that number to high powers, and we might be loose significant precision in the calculation.
With that in mind, the following is a chart of the data.
The first 3 data points (in red) are far off the linear trendline that closely fits the remaining data (in blue).
As a practical matter, we should exclude the 1st data point (C2, E2) because it precedes the date when the fuel tank was last topped off.
I would also exclude the 2nd and 3rd data points (C3:C4, E3:E4), since they appear to be "outliers".
But arguably, if we include the 2nd and 3rd data points, the resulting trendline is not too much different. The choice is yours to make.
In any case, since a linear trendline does indeed fit the data well, we can use the dates in column C for the "known Y" values in formulas, instead of the relative day numbers.
And that justifies our use of FORECAST.
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Some unrelated observations....
1. Your formulas in column E and F can be simplified, to wit:
E2: =IF(
D2=0, NA(), 59*22*D2*0.0195478)
F4: =IF(
E4=0, NA(), E3-E4)
2. Is 0.0195478 correct for your purposes?
To convert cubic inches to liters, we should multiply by
0.016387064 = 25.4^3 * 1E-6.