The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs., find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present. [Given `log_e3=1. 0986 ,\ e^(2. 1972)=9` ]

Explanation

Let ' `P` ' be the number of bacteria present at time ' `t` '


Given


`frac{d {P}}{d t} propto mathbf{P}`


`Rightarrow frac{d {P}}{d t}=k mathbf{P}` ................[because {k} is constant]


`int frac{d mathbf{P}}{mathbf{P}}=k int d t`


`log {P}=k t+c`


`{P}={e}^{k {t}-c} `


`{P}={e}^{k t} c ldots(1)`


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