(D) Given the differential equation: $\frac{d p}{d t} = 0.5 p - 450 = 0.5(p - 900)$.Separating the variables, we get: $\frac{d p}{p - 900} = 0.5 dt$.I

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(D) Given the differential equation: $\frac{d p}{d t} = 0.5 p - 450 = 0.5(p - 900)$.Separating the variables, we get: $\frac{d p}{p - 900} = 0.5 dt$.Integrating both sides from $t=0$ to $t=T$ where $p(0)=850$ and $p(T)=0$:$\int_{850}^{0} \frac{d p}{p - 900} = \int_{0}^{T} 0.5 dt$.$[\ln |p - 900|]_{850}^{0} = 0.5 T$.$\ln |0 - 900| - \ln |850 - 900| = 0.5 T$.$\ln(900) - \ln(50) = 0.5 T$.$\ln(\frac{900}{50}) = 0.5 T$.$\ln(18) = 0.5 T$.$T = 2 \ln(18)$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation $\frac{d p(t)}{d t}=0.5 p(t)-450$. If $p(0)=850$, then the time at which the population becomes zero is

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A
$\log 9$
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$\frac{1}{2} \log 18$
C
$\log 18$
D
$2 \log 18$

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The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation $\frac{d p(t)}{d t}=0.5 p(t)-450$. If $p(0)=850$, then the time at which the population becomes zero is

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