Curve Fitting and interpolation

Please see the attached two curves which i want to transfer to excel to automate my
calculations, i made a try in the attached workbook and i need your advice and comments

for the first curve
having t,x i got y
now, is what i have done is true and accurate (using the linear equation) or there a best fit polynomial or other way to do that
I tried LINEST on the rows A3 to A8 if i complete to A33 will it differ or be more accurate
if i have t=12 (or any value between 0,30 which have no exact values on the attached curve) and x =14.5 for example how can i interpolate to find y

with the same x i got y in the curve in the second sheet
is my polynomial is accurate , is there a better way
thanks in advance

I tried LINEST on the rows A3 to A8 if i complete to A33 will it differ or be more accurate

It will be more accurate, but you need to remove the rows that don't have data.

if i have t=12 (or any value between 0,30 which have no exact values on the attached curve) and x =14.5 for example how can i interpolate to find y

Use the slope and offset returned from LINEST in cells N29 and O29 respectively.

is my polynomial is accurate , is there a better way

It's certainly accurate as to the data; with a third-order polynomial you can fit ANY four points having unique domain (x) values. That doesn't mean it's correct.

thank you very much for your reply , please have a look for that

Use the slope and offset returned from LINEST in cells N29 and O29 respectively.

but the slope and offset returned from LINEST in cells N29 and O29 is belongs to linear t=0

when i use them it gives the point shown in the graph, the green triangle located in t=0 where
i look for a line in between 0,30 say t=15

thanks in advance