Expression 9: "p" Subscript, "i" "n" "t" "e" "g" "r" "a" "l" , Baseline left parenthesis, "x" , right parenthesis equals negative StartFraction, "p" Subscript, 0 , Baseline "r" left parenthesis, left parenthesis, 1 minus "k" , right parenthesis Superscript, "t" minus StartNestedFraction, "x" NestedOver "r" , EndNestedFraction , Baseline minus left parenthesis, 1 minus "k" , right parenthesis Superscript, "t" , Baseline , right parenthesis Over ln left parenthesis, 1 minus "k" , right parenthesis , EndFraction Has graph. To audio trace, press ALT+T.pintegralx=−p0r1−kt−xr−1−ktln1−k
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Expression 10: "x" Subscript, "t" "o" "Y" , Baseline left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline , "x" Subscript, "b" "o" "u" "g" "h" "t" , Baseline , right parenthesis equals "p" Subscript, "i" "n" "t" "e" "g" "r" "a" "l" , Baseline left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline plus "x" Subscript, "b" "o" "u" "g" "h" "t" , Baseline , right parenthesis minus "p" Subscript, "i" "n" "t" "e" "g" "r" "a" "l" , Baseline left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis You've defined 'p_integral' in more than one place. Try deleting some of the definitions of 'p_integral'.xtoYxstart,xbought=pintegralxstart+xbought−pintegralxstart
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Expression 11: "x" Subscript, "t" "o" "Y" "a" "l" "t" , Baseline left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline , "x" Subscript, "b" "o" "u" "g" "h" "t" , Baseline , right parenthesis equals StartFraction, "p" Subscript, 0 , Baseline "r" Over ln left parenthesis, 1 minus "k" , right parenthesis , EndFraction times left parenthesis, left parenthesis, 1 minus "k" , right parenthesis Superscript, "t" minus StartFraction, "x" Subscript, "s" "t" "a" "r" "t" , Baseline Over "r" , EndFraction , Baseline minus left parenthesis, 1 minus "k" , right parenthesis Superscript, "t" minus StartFraction, "x" Subscript, "s" "t" "a" "r" "t" , Baseline plus "x" Subscript, "b" "o" "u" "g" "h" "t" , Baseline Over "r" , EndFraction , Baseline , right parenthesis Subscripts may only contain letters and digits. ' ' is not allowed.xtoYaltxstart,xbought=p0rln1−k·1−kt−xstartr−1−kt−xstart+xboughtr
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Expression 12: "Y" Subscript, "t" "o" "X" , Baseline left parenthesis, "x" , right parenthesis equals "r" times StartFraction, ln left parenthesis, StartNestedFraction, left parenthesis, "p" Subscript, 0 , Baseline times "r" times "e" Superscript, left parenthesis, left parenthesis, "r" times "t" minus "x" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis times StartNestedFraction, ln left parenthesis, 1 minus "k" , right parenthesis NestedOver "r" , EndNestedFraction , right parenthesis , Baseline , right parenthesis NestedOver "p" Subscript, 0 , Baseline times "r" times left parenthesis, 1 minus "k" , right parenthesis Superscript, StartNestedFraction, left parenthesis, "r" times "t" minus "x" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis NestedOver "r" , EndNestedFraction , Baseline minus "x" times ln left parenthesis, 1 minus "k" , right parenthesis , EndNestedFraction , right parenthesis Over ln left parenthesis, 1 minus "k" , right parenthesis , EndFraction Has graph. To audio trace, press ALT+T.YtoXx=r·lnp0·r·er·t−xstart·ln1−krp0·r·1−kr·t−xstartr−x·ln1−kln1−k
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Expression 13:
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Expression 14:
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Expression 15: "y" Subscript, "p" "a" "i" "d" , Baseline left parenthesis, "x" , right parenthesis equals "r" times left parenthesis, negative StartFraction, left parenthesis, ln left parenthesis, 1 minus "x" times left parenthesis, left parenthesis, StartNestedFraction, ln left parenthesis, 1 minus "k" , right parenthesis NestedOver "r" times "p" Subscript, 0 , Baseline times left parenthesis, 1 minus "k" , right parenthesis Superscript, left parenthesis, "t" minus StartNestedFraction, "x" NestedOver "r" , EndNestedFraction , right parenthesis , Baseline , EndNestedFraction , right parenthesis , right parenthesis , right parenthesis , right parenthesis Over ln left parenthesis, 1 minus "k" , right parenthesis , EndFraction , right parenthesisypaidx=r·−ln1−x·ln1−kr·p0·1−kt−xrln1−k
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Expression 16:
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Expression 17: "p" Subscript, "i" "n" "t" "e" "g" "r" "a" "l" Subscript, "w" "r" "o" "n" "g" , Baseline , Baseline left parenthesis, "x" , right parenthesis equals negative StartFraction, "p" Subscript, 0 , Baseline "r" left parenthesis, left parenthesis, 1 minus "k" , right parenthesis Superscript, "t" minus StartNestedFraction, "x" NestedOver "r" , EndNestedFraction , Baseline , right parenthesis Over ln left parenthesis, 1 minus "k" , right parenthesis , EndFraction Subscripts may only contain letters and digits. '_{wrong}' is not allowed.pintegralwrongx=−p0r1−kt−xrln1−k
