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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "p. 100  25, 26  [both abou
t carbon dating] " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 347 "25:  Assumptions are half-life of carbon-14 is 56
00 yr, and that 2% of a sample remain.  How old is the sample if the c
osmic proportion of C-14 was present when it was formed.   (According \+
to my wife who is a geophycist, several inaccuracies are present in th
e discussion, but that does not change the mathematical model based on
 the assumptions.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "resta
rt: d25:=diff(A(t),t)=alpha*A(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "s25:=dsolve(\{d25,A(0)=Ao\},A(t));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "s25a:=subs(t=5600,rhs(s25));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a25:=solve(s25a=Ao/2,alpha);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "solve(rhs(subs(alpha=a25,s25
))=Ao/20,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 178 "26.  This is an easy adoption o
f the code above.  However, I question their use of \"error.\"  If you
 change 2% to 3% there is no way to call that a 1% error.  That is a 5
0% error." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
74 "p. 114  3, 4, 9, 24, 25 .......... 5 first  (not assigned but inte
resting)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart; g:=981
/100; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "d5:=m*diff(v(t),t
)=m*g-k*v(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "m:=5; k:=1
0; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "s5:=dsolve(\{d5,v(0)
=50\}, v(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "x5:=int(rh
s(s5), t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(x5+9019/
400,t=0..100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(x5
+9019/400=500,t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "3." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "restart; g:=981/100; m:=500; k:=50;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 50 "dsolve(\{m*diff(v(t),t)=m*g-k*v(t), v(0)=
0\}, v(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x3:=int(rhs(
%),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fsolve(x3-981=100
0,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(x3-981,t=0..2
0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "restart; #4\ng:=32; \+
m:=400/g; k:=10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "dsolve(
\{m*diff(v(t),t)=m*g-k*v(t), v(0)=0\}, v(t));" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "x4:=int(rhs(%),t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "fsolve(x4-50=30,t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(x4-50,t=0.
.2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "restart; #9 with t
errible assumptions about water resistance\nm:=100; g:=981/100; bf:=-g
*m/40; k:=10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "v9:=dsolve
(\{m*diff(v(t),t)=m*g+bf-k*v(t), v(0)=0\}, v(t));" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 19 "x9:=int(rhs(v9),t);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 17 "em9:=x9-38259/40;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "fsolve(rhs(v9)=70,t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(rhs(v9),t=
0..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "restart; #24\nd2
4:=(mo-alpha*t)*diff(v(t),t)-alpha*beta=-g*(mo-alpha*t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "v24:=rhs(dsolve(\{d24,v(0)=0\},v(t)
));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "x24:=int(v24,t);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x240:=simplify(subs(t=0,x24
));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "ht24:=x24-x240;  # h
ave to make height(0)=0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "#25 is
 standard in physics; I'm sure you have done it." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "p. 128  8, 19   Note the \+
misprint in 8 [should be " }{XPPEDIT 18 0 "N = 4;" "6#/%\"NG\"\"%" }
{TEXT -1 8 " not 8]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f:=
(x,y)->(y^2+y)/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "ieul:
=proc(xo, yo, N, h)\nlocal i, F, G:\nglobal x, y:\nx:=xo:\ny:=yo:\nfor
 i to N do\n  F:=evalf(f(x,y)):\n  G:=evalf(f(x+h,y+h*F)):\n  y:=evalf
(y+h*(F+G)/2):\n  x:=evalf(x+h):\nod:\nprint(x,y);\nend:" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 
"ieul(1,1,4,0.2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "eul:=
proc(xo, yo, N, h)\nlocal i:\nglobal x, y:\nx:=xo:\ny:=yo:\nfor i to N
 do\n  y:=evalf(y+h*f(x,y)):\n  x:=evalf(x+h):\nod:\nprint(x,y);\nend:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eul(1,1,4,0.2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "x:='x': y:='y': de:=diff(y(x
),x)=f(x,y(x));\ndsolve(\{de,y(1)=1\}, y(x));" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 60 "So the true answer at 1.8 is 9.  Let me try this again
 with " }{XPPEDIT 18 0 "N = 8;" "6#/%\"NG\"\")" }{TEXT -1 1 "." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ieul(1,1,8,0.1);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ieul(1,1,16,0.05);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ieul(1,1,80,0.01);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 148 "Still not great!  Note:  All those evalf
's are necessary.  Try leaving the ones for  y:=  and  x:= off and do \+
80 steps.  (But save your work first!)" }}}}{MARK "50" 0 }{VIEWOPTS 1 
1 0 1 1 1803 }