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The population p(t) at time t of a certa...

The population p(t) at time t of a certain mouse species satisfies the differential equation `(d p(t))/(dt)=0. 5 p(t)-450` If `p(0)""=""850` , then the time at which the population becomes zero is (1) 2 ln 18 (2) ln 9 (3) `1/2` In 18 (4) ln 18

Text Solution

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`p(0)= 850`
`(dp(t))/dt= 0.5p(t) - 450`
`int (dp(t))/(0.5p(t) - 450) = int dt`
`= 1/0.5 ln|0.5 p(t) - 450| = t`
`= 2[ln 450 - ln 25] = t`
`= 2 ln(450/25) `
`= 2 ln 18 = t`
option 1 is correct
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