Browse Questions

# The growth rates of a bacteria population is proportional to its size. Initially the population is $10,000$ while after 10 days its size is $25,000$ . What will be population after 20 days?

$(a)\;100(2.5)^2 \\ (b)\;1000(2.5)^2 \\ (c)\;2500 \\ (d)\;250$
Can you answer this question?

According to given condition $\large\frac{dP}{dt}=$$KP \int \large\frac{dP}{P}$$= K \int dt$
$\log P \bigg ]_{10000}^{25000}=K t \bigg]_0^{10}$
$\log 2.5 =10.K$
$K= \large\frac{\log 2.5 }{10}$
$\log P\bigg]_{10000}^{P}=\large\frac{\log 2.5}{10} \times t \bigg]_0^{20}$
$\log \large\frac{P}{10000} =\large\frac{\log 2.5}{10}$$\times 20 \log \large\frac{P}{10000}$$=\log (2.5)^2$