I have this equation I am trying to solve and verify for a project, I am unabled to see what I'm doing wrong as I solve this equation. Been scratching my head for hours, I swear I did it right? If you have interest on what these equations do, look here 3 Process Model Please note, this is only the first equation located at the link(solve for ss).
Here is my work:
taw: 15
tas: 9
e: 2.718281828459
la: 2.4
ha: 14.3
g: -0.3813
d: -0.0353
PART 1: Solve For SW
Step 1 SW=ha-(ha-SS)*e^(g*tas)
Step 2 SW=14.3-(14.3-SS)*2.718281828459^(-0.3813*9)
Step 3 SW=14.3-(14.3-SS)*2.718281828459^(-3.4317)
Step 4 SW=14.3-(14.3-SS)*0.032331929746214
Step 5 SW=14.3-(0.46234659537086-0.032331929746214SS)
Step 6 SW=14.3-0.46234659537086-0.032331929746214SS
Step 7 SW=13.837653404629-0.032331929746214SS
PART2: Solve For SS
Step 1 SS=la+(SW-la)*e^(d*taw)
Step 2 SS=2.4+(13.837653404629-0.032331929746214SS-2.4)*2.718281828459^(-0.0353*15)
Step 3 SS=2.4+(13.837653404629-0.032331929746214SS-2.4)*2.718281828459^(-0.5295)
Step 4 SS=2.4+(13.837653404629-0.032331929746214SS-2.4)*0.58889934575108
Step 4 SS=2.4+(8.1489850367163-0.032331929746214SS-1.4133584298026)
Step 5 SS=9.1356266069137-0.032331929746214SS
Step 6 SS+0.032331929746214SS=9.1356266069137-0.032331929746214SS+0.032331929746214SS
Step 7 1.0323319297462SS=9.1356266069137
Step 8 1.0323319297462SS / 1.0323319297462=9.1356266069137 / 1.0323319297462
Step 9 SS=8.8495050319325
PART 3: Check SW Work
Step 1 SW=ha-(ha-SS)*e^(g*tas)
Step 2 SW=14.3-(14.3-8.8495050319325)*2.718281828459^(-0.3813*9)
Step 3 SW=14.3-(5.4504949680675)*2.718281828459^(-3.4317)
Step 4 SW=14.3-(5.4504949680675)*0.032331929746214
Step 5 SW=14.3-0.17622502038965
Step 6 SW=14.12377497961
PART 4: Check SS Work
Step 1 SS=la+(SW-la)*e^(d*taw)
Step 2 SS=2.4+(14.12377497961-2.4)*2.718281828459^(-0.0353*15)
Step 3 SS=2.4+(11.72377497961)*2.718281828459^(-0.0353*15)
Step 4 SS=2.4+(11.72377497961)*2.718281828459^(-0.5295)
Step 5 SS=2.4+(11.72377497961)*0.58889934575108
Step 6 SS=2.4+6.9041234152254
Step 7 SS=9.3041234152254 <---This value should be same as in PART 2
As far as I can tell , you have two linear equations in the variables $SS$ and $SW$: $$ \eqalign{{\it SW}&={\it ha}-({\it ha}-{\it SS})\,{{\rm e}^{g\; {\it tas}}}\cr {\it SS}&={\it la}+ \left( {\it SW}-{\it la} \right) {{\rm e}^{d\;{\it taw}}}}$$
The solution of these would be $$ {\it SS}={\frac {{{\rm e}^{d\;{\it taw}+g\;{\it tas}}}\it{ha}- {{\rm e}^{d\;{\it taw}}}{\it ha}+{{\rm e}^{d\;{\it taw}}}{\it la}-{\it la} }{{{\rm e}^{d\;{\it taw}+g\;{\it tas}}}-1}},{\it SW}={\frac {{ {\rm e}^{d\;{\it taw}+g\;{\it tas}}}{\it la}+{{\rm e}^{g\;{\it tas}}}{\it ha}-{ {\rm e}^{g\;{\it tas}}}{\it la}-{\it ha}}{{{\rm e}^{d\;{\it taw}+g\;{\it tas }}}-1}} $$ You didn't tell us what $g$ and $d$ were, but you seem to be using $g=-0.3813$ and $d=-0.0353$. Substituting in these and your values for the other constants, you should get approximately $$ SS = 9.312947477, SW = 14.13875897$$ which is not what you got.