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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "                          \+
                                  James and Jeremy's Problem" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "# 14      p, 81" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 62 "In the Malthusian law the equation is like this:  P(t)=Po e^kt
" }}{PARA 0 "" 0 "" {TEXT -1 78 "First you have to know P(0), in this \+
case it is P(0)=(300)e^kt, because Po=300" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 61 "In 10 years (1980) the population of alligators grew to 1500." 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "So now we solve for the constan
t k." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "p:=unapply(300*exp(k*t),t
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pGR6#%\"tG6\"6$%)operatorG%&
arrowGF(,$-%$expG6#*&%\"kG\"\"\"9$F2\"$+$F(F(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "k:=solve(p(10)=1500,k);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"kG,$-%#lnG6#\"\"&#\"\"\"\"#5" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 85 "Now that we have the constant k, we need to solve fo
r P(30) to find the pop. in 2000." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "p(30);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#\"&+v$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 107 
"Therefore, in the year 2000 (t=30) the population of alligators at th
e Kennedy Space Center would be 37500." }}{PARA 0 "" 0 "" {TEXT -1 52 
"This answer agrees with the answer we found by hand." }}}}{MARK "0 0 \+
0" 43 }{VIEWOPTS 1 1 0 1 1 1803 }