The rate of growth of a population is proportional to the number present. if the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000? [Given, `log_e 5 = 1.609` , `log_e 2 = 0.6931` . ]

Explanation

``
`frac{{dp}}{{dt}} propto {p}`


`Rightarrow frac{{dp}}{{dt}}={kp} quad text { (where } {k} text { is constant) }`


`Rightarrow int frac{{dp}}{{dt}}=int {kdt}`


`Rightarrow ln {p}={kt}+{c} text { (on integrating both sides) } `


`text { At } {t}=0, {p}=(1 / 2) {lac}=50,000 . `


`text { At } {t}=25, {p}=(1 / 2) {lac}=1,00,000 .`


`therefore text { we get, } {c}=ln (50,000) text { and } {k}=ln (2) / 25`


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