Question

The population p(t) at time t of a certain mouse species satisfies the differential equation $fraction numerator dp space left parenthesis straight t right parenthesis over denominator dt end fraction space equals space 0.5 space left parenthesis straight t right parenthesis space minus 450$ . if p (0) = 850, then the time at which the population becomes zero is

2 log 18

log 9

$1 half space log space 18$

log 18

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Solution

2 log 18

fraction numerator straight d left parenthesis straight p left parenthesis straight t right parenthesis right parenthesis over denominator dt end fraction space equals space 1 half straight p left parenthesis straight t right parenthesis space minus 450 fraction numerator begin display style straight d left parenthesis straight p left parenthesis straight t right parenthesis right parenthesis end style over denominator begin display style dt end style end fraction space equals space fraction numerator straight p space left parenthesis straight t right parenthesis minus 900 over denominator 2 end fraction 2 integral fraction numerator straight d left parenthesis straight p left parenthesis straight t right parenthesis right parenthesis over denominator straight p left parenthesis straight t right parenthesis minus 900 end fraction equals integral dt 2 space ln space vertical line straight p left parenthesis straight t right parenthesis minus 900 vertical line space equals space straight t plus straight c straight t equals 0 rightwards double arrow space 2 space ln space 50 space equals space 0 plus straight c therefore space 2 space ln space vertical line straight p left parenthesis straight t right parenthesis minus 900 vertical line space equals space straight t space plus space 2 space ln space 50 straight p left parenthesis straight t right parenthesis space equals space 0 space rightwards double arrow 2 space ln space 900 space equals space straight t plus 2 space ln space 50 straight t space equals space 2 space left parenthesis In space 900 minus In space 50 right parenthesis space equals space 2 space ln space open parentheses 900 over 50 close parentheses space equals space 2 space ln space 18

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Continuity And Differentiability

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Continuity And Differentiability

The population p(t) at time t of a certain mouse species satisfies the differential equation . if p (0) = 850, then the time at which the population becomes zero is 2 log 18 log 9 log 18

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation