COMEDK · Maths · 32. Differential Equations
In a bank the principal increases continuously at the rate of 4% per annum. In how many years will ₹1000 triple itself?
- A \(\dfrac{1}{25}\log_e 3\)
- B \(25\log_e 3\)
- C \(\log_e 75\)
- D \(\dfrac{25}{\log_e 3}\)
Answer & Solution
Correct Answer
(B) \(25\log_e 3\)
Step-by-step Solution
Detailed explanation
Let \(P\) be the principal at any time \(t\). The rate of increase of principal is given by \(\dfrac{dP}{dt} = \dfrac{4}{100}P\) \(\dfrac{dP}{P} = 0.04 dt\) Integrating both sides: \(\int \dfrac{dP}{P} = \int 0.04 dt\) \(\log_e P = 0.04 t + C\) At \(t = 0\), \(P = 1000\), which…
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