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In a bank, principal increases continuou...

In a bank, principal increases continuously at a rate of 10% per year. In how many years Rs 1000, doubles itself ?

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Let P be the principal at any time t. According to the given problem,
`(dP)/(dt) = (10)/(100) xx P`
`rArr (dP)/(P) = (dt)/(10)`
Integrating both sides, we get
`In|P| = (t)/(10) + InC`
`P = Ce^((1)/(10))`
at `t = 0, P = 1000`
`rArr 1000 = C`
`:. P = 1000 e^(t//10)`
If it is doubled in time t then `2000 = 1000 e^(t//10)`
`rArr e^(t//10) = 2`
`rArr (t)/(10) In 2`
`t = 10 In 2`
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