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

Options

A. 2 ln 18
B. ln 9
C. `1/2` ln 18
D. ln 18

Answer

A

Explanation

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