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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

A

2 ln 18

B

ln 9

C

`1/2` ln 18

D

ln 18

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `2(dp(t))/(900-p(t))=-dt`
Integrating, we get
`-2"ln "(900-p(t))=-t+c`
when `t=0, p(0)=850`
`therefore -2" ln "(50/(900-p(t)))=-t`
`therefore 900-p(t)=50e^(t//2)`
Let `p(t_(1))=0`
`therefore 0=900-50e^(t//2)`
`therefore t_(1)=2` ln 18
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