{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 184 "Exercise: The average ann ual rate r (in percent form) for commercial bank credit cards from 199 0 through 1995 can be modeled by the following function r(t), where t =0 represents 1990." }}{PARA 0 "" 0 "" {TEXT -1 64 "(a) Find the deriv ative function of this interest rate function." }}{PARA 0 "" 0 "" {TEXT -1 175 "(b) How do we find the year which interest rate decrease s the most? Estimate such year.\n(c) How do we find the year which int erest rate increases the most? Estimate such year." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "r:=t->sqrt(1.01*t^4-6.72*t^3+4.85*t^2+2.4*t +330.26);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "r1:=t->diff(r( t),t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(r1(t),t=0..6 ,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fsolve(r1(t)= 0,t,0..1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 133 "Before we sketch y = r(t), we predict that the interest rate hits the highest level when t is about 0.753, which is before year 1991." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "fsolve(r1(t)=0,t,4..5);" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "Before we skech y = r(t), we predict th at the interest rate hits the lowest level when t is about 4.42, which is near the middle of 1994." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(r(t),t=0..6,y=0..20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 46 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }