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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT -1 34 "A Mathematical Model for Diffusion" }{MPLTEXT 0 21 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 31 "\nPoint plot of the data points\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 559 "pointplot([[0.0,\01169.32386589],[1.0,
\011421.1427639],[2.0,\011688.0393743],[3.0,\011911.6064838],[4.0,\011
1080.586782],\n[5.0,\0111207.09845],[6.0, 1301.55283],[7.0,\0111372.61
5398],[8.0,\0111426.339919],[9.0,\0111467.935616],\n[10.0,\0111499.127
065],[11.0,\0111525.123488],[12.0,\0111545.059047],[13.0,\0111561.5170
61],[14.0,\0111572.787146],\n[15.0,\0111583.184296],[16.0, 1590.983932
],[17.0, 1597.051893],[18.0,1603.112758],[19.0,\0111606.583206],\n[20.
0,\0111610.912394],[21.0, 1615.24868],[22.0, 1616.114518],[23.0, 1617.
846193],[24.0, 1619.577869],\n[25.0,\0111620.443706],[26.0, 1621.30954
4]],symbol=circle);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 432 "A
1:=421.1427639;A2:=688.0393743;A3:=911.6064838;A4:=1080.586782;A5:=120
7.09845;A6:=1301.55283;A7:=1372.615398;A8:=1426.339919;A9:=1467.935616
;A10:=1499.127065;A11:=1525.123488;A12:=1545.059047;A13:=1561.517061;A
14:=1572.787146;\nA15:=1583.184296;A16:=1590.983932;A17:=1597.051893;A
18:=1603.112758;A19:=1606.583206;A20:=1610.912394;A21:=1615.24868;A22:
=1616.114518;A23:=1617.846193;A24:=1619.577869;\nA25:=1620.443706;A26:
=1621.309544;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {MPLTEXT 0 21 27 "Calculating the constants \n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 20 "A:=(n)->c/2-c/2*a^n;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 26 "eq1:=A(2)-A2;eq2:=A(3)-A3;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 28 "sol:=solve(\{eq1,eq2\},\{a,c\});" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "a:=.7551969728;c := 3202.584
834;" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 45 "\nA comparison betwe
en the data and the model\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
562 "P1:=pointplot([[0.0,\01169.32386589],[1.0,\011421.1427639],[2.0,
\011688.0393743],[3.0,\011911.6064838],[4.0,\0111080.586782],\n[5.0,
\0111207.09845],[6.0, 1301.55283],[7.0,\0111372.615398],[8.0,\0111426.
339919],[9.0,\0111467.935616],\n[10.0,\0111499.127065],[11.0,\0111525.
123488],[12.0,\0111545.059047],[13.0,\0111561.517061],[14.0,\0111572.7
87146],\n[15.0,\0111583.184296],[16.0, 1590.983932],[17.0, 1597.051893
],[18.0,1603.112758],[19.0,\0111606.583206],\n[20.0,\0111610.912394],[
21.0, 1615.24868],[22.0, 1616.114518],[23.0, 1617.846193],[24.0, 1619.
577869],\n[25.0,\0111620.443706],[26.0, 1621.309544]],symbol=circle):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "P2:=plot(c/2-c/2*a^n,n=
0..26,color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "displa
y(P1,P2);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 42 "\nCalculating e
rrors for a particular base\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "Ap:=(n)->c/2-c/2*a^n;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
57 "for n from 1 to 20 do\nERR:=abs((A||n-Ap(n))/A||n*100);od;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 78 "\nYour turn - try another pair of numbers (you need \+
to replace # with numbers)\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "a:='a';c:='c';n:='n';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "eq1:=A(#)-A#;eq2:=A(#)-A#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 28 "sol:=solve(\{eq1,eq2\},\{a,c\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "a:=#;c:=#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
562 "P1:=pointplot([[0.0,\01169.32386589],[1.0,\011421.1427639],[2.0,
\011688.0393743],[3.0,\011911.6064838],[4.0,\0111080.586782],\n[5.0,
\0111207.09845],[6.0, 1301.55283],[7.0,\0111372.615398],[8.0,\0111426.
339919],[9.0,\0111467.935616],\n[10.0,\0111499.127065],[11.0,\0111525.
123488],[12.0,\0111545.059047],[13.0,\0111561.517061],[14.0,\0111572.7
87146],\n[15.0,\0111583.184296],[16.0, 1590.983932],[17.0, 1597.051893
],[18.0,1603.112758],[19.0,\0111606.583206],\n[20.0,\0111610.912394],[
21.0, 1615.24868],[22.0, 1616.114518],[23.0, 1617.846193],[24.0, 1619.
577869],\n[25.0,\0111620.443706],[26.0, 1621.309544]],symbol=circle):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "P2:=plot(c/2-c/2*a^n,n=
0..26,color=red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "displa
y(P1,P2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "for n from 1 t
o 20 do\nERR:=abs((A||n-Ap(n))/A||n*100);od;" }}}}{MARK "27 0 0" 57 }
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