questiontype=0
cols=15
rows=5
inputs=1
n=$counter
mytexsize=+4

question$n=!record 77 of lang/remarks.$taal
varlist=t
mathviewpanel=$module_title:H(t)=
#@Schrijf de onderstaande exponenti&euml;le functie<br> in de <em>algemene vorm</em>: H(t)=b&times;g<sup>t</sup> 
checkfile=exos/checkfile3.proc

!if $level=0
    R=$counter
!else
    R=$level
!endif

!if $R=1
    #kan exact
    g=!randitem 2,3,4,5,6,7,8,9
    a=!randitem 2,3,4,5,6,7,8,9
    b=!randitem 1,2,3,4
    formula$n=H(t)\,\,=\,\,$a\cdot $g^{t+$b}
    answer$n=$[$a*$g^$b]*$g^t
    c=$[$a*$g^$b]
    texanswer$n=$a\cdot$g^{t + $b} \,=\, $a \cdot $g^{t}\cdot $g^{$b} \,=\, $a\cdot $g^{$b}\cdot $g^{t} \,=\, $c \cdot $g^{t}
 !exit
!endif

!if $R=2
    # hoeft niet exact
    keuze=!randitem 1,2
    keuze=2
    !if $keuze=1
	b=!randitem +1,+2,+3,+4,-1,-2,-3,-4
	a=!randint 5,25
	g=!randitem 2,3,4,5,6,7,8,9
	c=!exec pari printtex($a*$g^($b))
	formula$n=H(t)\,\,=\,\,$a\cdot $g^{t $b}
	answer$n=$[$a*$g^$b]*$g^t
	texanswer$n=$a\cdot$g^{t $b} \,=\, $a \cdot $g^{t}\cdot $g^{$b} \,=\, $a\cdot $g^{$b}\cdot $g^{t} \,=\, $c \cdot $g^{t}
    !else
	b=!randitem -2,-3,-4,-5,-6
	a=!randint 5,25
	g=!randitem 2,3,4,5,6,7,8,9
	tot=!exec pari A=$g^($b)\
	printtex(A)
	c=!line 2 of $tot
	gc=!line 1 of $tot
	formula$n=H(t)\,\,=\,\,$a\cdot $g^{$b \cdot t}
	answer$n=$a*$gc^t
	texanswer$n=$a\cdot$g^{$b \cdot t} \,=\, $a \cdot \left( $g^{$b} \right)^{t} \,=\, $a \cdot $c^{t}    
    !endif
 !exit
!endif

!if $R=3
    g=!randitem 2,3,4,5,6
    a=!randitem 1/2,1/4,1/5,2,3,4
    b=!randitem 1,2,3,4,5
    c=!randitem 1,2,3,4,5
    tot=!exec pari A=($a)*$g^($b)\
    printtex(A)\
    B=$g^(-1*$c)\
    printtex(B)\
    printtex($a)
    
    A=!line 1 of $tot
    At=!line 2 of $tot
    B=!line 3 of $tot
    Bt=!line 4 of $tot
    at=!line 5 of $tot
    answer$n=$A*$B^t
    formula$n=H(t)\,\,=\,\,$at \cdot $g^{$b - $c \cdot t}
    texanswer$n=$a\cdot $g^{$b} \cdot $g^{-$c\cdot t} = $At \cdot\left( $Bt\right)^{t}
 !exit
!endif

!if $R>3
    g=!randitem 1/2,1/3,2/3,1/4,3/4,1/5,2/5,3/5,4/5,1/6,5/6
    tot=!exec pari printtex($g)\
    A=1/($g)\
    printtex(A)
    gt=!line 1 of $tot
    f=!line 2 of $tot
    ft=!line 3 of $tot
    a=!randitem 5,10,15,20,25,30
    answer$n=$a*($f)^t
    formula$n=H(t)\,\,=\,\,\frac{$a}{\left($gt\right)^{t}}
    texanswer$n=H(t)=$a\cdot \left( $ft \right)^{t}
 !exit
!endif

